e) A student spent 50 minutes doing her homework. She spent m minutes doing Geography. 2m minutes doing Mathematics and the remaining (m + 7) minutes studying History. How many minutes did she spend doing Mathematics? ​

The transverse axis has a length of 5 units.

A transverse axis is a line that divides a conic section (such as an ellipse or hyperbola) into two symmetric parts. In the case of an ellipse, the transverse axis is the major axis, and it runs perpendicular to the minor axis.

To find the length of the transverse axis, we can use the equation (x − 1)²/a² + (y + 3)²/b² = 1, where a and b are the lengths of the major and minor axes, respectively.

The given equation is :

(x−h)²/a² + (y−k)²/b² = 1

Where h and k are the coordinates of the center of the ellipse.

Now we can substitute the given values in the equation

(x−1)²/25 + (y+3)²/9 = 1

To find the length of the transverse axis, we can take square root of the major axis value, a² = 25

√25 = 5

So the length of the transverse axis is 5 units.

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Consequently, b must have a value of -3.The following points should be located on the cartesian plane: (0,a), (a,0), (-a, 0), (0,-a)..

How to calculate a line's equation given two points:Make use of the slope formula to determine the slope.

To find the y-intercept (b), use one of the points and the slope.

The slope-intercept form of a line is y = mx + b, and you may obtain the equation for the line by plugging in the values for m and b once you have those values.

On the graph of 2x + 3y = - 5, 2,b) is located.

To estimate

The amount b

Given that (2,b) is located on the graph of 2x + 3y = 5,

hence, we do

( 2 × 2 ) + ( 3 × b ) = - 5

⇒ 4 + 3b = - 5

⇒ 3b = - 9

⇒b = - 3

Consequently, b must have a value of -3.

The following points should be located on the cartesian plane: (0,a), (a,0), (-a, 0), (0,-a)...

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The value of the expression when e = 12 and f = 1/2 is 1

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

e/4 + 2f - 3

Also, from the question, we have the following values:

e = 12 and f = 1/2

substitute the known values in the above equation, so, we have the following representation

e/4 + 2f - 3 = 12/4 + 2 * 1/2 - 3

Evaluate the expression

e/4 + 2f - 3 = 1

Hence, the solution is 1

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The number of solutions for given three system of linear equations.

We can simply solve this numerical problem by using the following process.

3x - y = 4 ==> a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

What is meant by numerical?

Based on the formula is:

Let the system of equations be a₁x + b₁y = c₁ and  a₂x + b₂y = c₂ then

Condition for One solution: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

Condition for No Solution:  a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Condition for infinitely many solutions:  a₁/a₂ = b₁/b₂ = c₁/c₂

Now in the given question:

a.) 3x - y = 4

6x - 2y = 8

⇒ a₁/a₂=3/6 = 1/2 ; b₁/b₂ = -1/-2 = 1/2 ; c₁/c₂ = 4/8 = 1/2

⇒  a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

The given system of equations is coincident lines, hence has infinitely many solutions.

b.) -3x + y = 7

     2x - 4y = -8

⇒ a₁/a₂= -3/2 ; b₁/b₂ = 1/-4 ; c₁/c₂ = 7/-8

⇒ a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

The given system of equations is intersecting lines, hence having a single solution.

c.) y = -4x - 5

y = -4x +1

⇒ a₁/a₂= -4/-4 = 1 ; b₁/b₂ = 1/1 = 1 ; c₁/c₂ = -5/1 = -5

⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂

The given system of equations is parallel lines, hence having no solution.

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The solution to the equation is 6.24

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

o/3.9=1.6

Express the variable as x for proper identification

So, we have the following representation

x/3.9=1.6

Multiply both sides of the equation by 3.9

This gives

x = 3.9 * 1.6

Evaluate

x = 6.24

Hence, the solution is 6.24

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Complete question

Solve the following equation

o/3.9=1.6

Answer:

  a1 = 16

  a(n) = a(n-1) -3   for n ≥ 2

Step-by-step explanation:

You want a recursive formula for the arithmetic sequence 16, 13, 10, 7, ....

The given sequence has a first term of 16. The common difference is ...

  13 -16 = -3

Each successive term is found by adding this difference to the one before. That describes the relation expressed by the recursive formula.

  [tex]\begin{cases}a_1=16\\a_n=a_{n-1}-3&\text{for $n\ge2$}\end{cases}[/tex]

The observational unit is Harley and the variable is 0, 1, 2, ..., 10.

When gathering statistical data, information is gathered and statistics are compiled on an observation unit, which is also known as a statistical unit occasionally. An observation is the value of a certain variable at a specific time.

The observational unit in this scenario is Harley and the variable is the number of times Harley chose the correct cup out of 10 trials. The variable can take on the values of 0, 1, 2, ..., 10, where 0 represents the number of incorrect choices and 10 represents the number of correct choices.

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Answer:

1.247 then 1.244 and finally 1.234

Step-by-step explanation:

The set of all differentiable real-valued functions defined on the real line. Proved that V is a vector space with the operations of addition and scalar multiplication defined as:

(f + g)(s) = f(s) + g(s)

(c f)(s) = c[f(s)].

Let V denote the set of all differentiable real-valued functions defined on the real line. Prove that V is a vector space with the operations of addition and scalar multiplication defined as:

(f + g)(s) = f(s) + g(s)

(c f)(s) = c[f(s)].

To prove vector space, we need to hold eight properties of vector space.

1) Closed

 (f + g)(s) = f(s) + g(s) (given)

so, closed holds with respect to given defined operation.

2) Associative law

let defined three function, f,g,h in V,

(f+g)(s)+h(s)=f(s)+g(s)+h(s)

                   = f(s)+(g+h)(s)

hence associative law hold.

3) Existence of identity,

(f+o)(s)=f(s)

f(s)+o(s)=f(s)

Hence, O(s) is identity for this function,

4) Existences of Inverse,

(-f)(s) is inverse for f(s)

5) Commutative law,

(f+g)(s)=(g+h)(s)

6)( cf)(s)=c[f(s)]g

7) c(f+g)(s)=cf(s)+g(s)

8) c(fg)(s)=(cf(s))g(s)

Hence, the given function is defined Operations.

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Erick and Mia both live the same distance from the park and decided to meet there one afternoon.

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As per the given scatter plot, if the outlier were removed, r would get closer to 1.

The term scatter plot in math is used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another

Here we have given that a local ice cream shop kept track of the number of cans of cold soda it sold each day and the temperature that day, for two months during the summer by using the scatter plot.

Here we have also know that X-axis is temperature measured in degrees Fahrenheit with a range from about 55 to 100 degrees and the value of Y-axis is the number of cans of soda sold with a range from about 165 to 195 cans.

While we take into consideration that a reasonable value of the correlation coefficient r for these data is 1.2.

Where as if the temperature were measured in degrees Celsius (C = 5/9 * (F - 32)), then the value of r would change accordingly.

Thus makes that the correlation coefficient would increase and be closer to 1.

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The equation of the graph that passes through the points (4, 24) and (6, 30) is y = 3x + 12

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

The point-slope form is expressed as;

y - y₁ = m( x - x₁ )

Given that the the graph passes through the points (4, 24) and (6, 30).

First, determine the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 30 - 24 )/( 6 - 4 )

Slope m = ( 6 )/( 2 )

Slope m = 3

Next, plug the slope m = 3 and point 1 ( 4,24) into the point-slope form and simplify.

y - y₁ = m( x - x₁ )

y - 24 = 3( x - 4 )

y - 24 = 3x - 12

y = 3x - 12 + 24

y = 3x + 12

Therefore, the equation of line is y = 3x + 12,

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The records about colors of automobiles on a car lot is a type of qualitative data.

Qualitative data consists of descriptions and characteristics that are difficult to quantify but easy to perceive in the human senses, such as smell, food, gender, country, and color. Observations, individual interviews, focus groups, and other similar procedures are used to get this information. Categorical data is another name for qualitative data in statistics; it refers to information that may be sorted into groups based on the characteristics of a given entity or event. Qualitative data are also known as categorical data since they may be sorted into categories.

When trying to determine the exact frequency of certain features or attributes, qualitative data is a very useful tool. It gives the statistician or the researcher the ability to generate parameters that can be used to examine larger data sets.

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For the given system of inequalities y < -x + a and y > x + b in the xy-plane , the solution represents the relation between a and b is given by :

Option A. a > b.

In the xy -plane given system of inequalities are :

y < -x + a

y > x + b

⇒ x + b < y < -x + a

⇒ x + b < -x + a

⇒ 2x < a - b

Now ( 0, 0 ) is the solution of the given system of inequalities represents :

2(0) < a - b

⇒ a - b > 0

⇒ a > b

Therefore, the relationship between the  'a' and 'b' for the given system of inequalities is given by :

Option A. a > b

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The radius of curvature is 1410 ft, the velocity is 5.48 ft/s, the normal acceleration is 0.0213 ft/s2, and the magnitude of the acceleration is 0.500 ft/s2 after the particle travels 30 ft along the path to (2.806, 142).

The radius of curvature, r, can be calculated using the formula r = v2/a, where v is the velocity and a is the normal acceleration. The velocity is calculated by integrating the acceleration with respect to time. The normal acceleration is calculated by taking the derivative of the velocity with respect to time. The magnitude of the acceleration is the same as the acceleration given in the problem.

1. Calculate the velocity, v, by integrating the acceleration (0.5 ft/s2) with respect to time:

v = 0.5 * t = 0.5 * 30 s = 15 ft/s

2. Calculate the normal acceleration, a, by taking the derivative of the velocity with respect to time:

a = dv/dt = 0.5 ft/s2

3. Calculate the radius of curvature, r, using the formula r = v2/a:

r = 15 ft/s2/0.5 ft/s2 = 30 ft = 1410 ft

4. The magnitude of the acceleration is the same as the acceleration given in the problem, 0.5 ft/s2.

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Here we are given that the distance between city A and B is 39miles and that between city B and C is 99miles . in order to find after how many miles we would reach the midpoint of city A and C , divide the total distance between A and C by 2 as ,

Total distance between A and C =[tex] d_{AB}+d_{BC}[/tex] = 39mi. + 99mi. = 138 miles

Divide this distance by 2 ,

138/2 = 69miles [ answer to Part A ]

_______________

Now the speed is 46miles/hr . In order to find time , use relation,

Speed * time = distance

So that,

time = distance/speed

time = 138/46

time = 3hrs [ answer to Part B ]

and we are done!

To make the dough, he'll need 5 3/4 cups of floor.

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a portion or part of a whole. It symbolizes the equal parts of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.

Here,

10 1/4 cups of flour needed to make a batch=41/4 cups

4 1/2 cups of floor is there=9/2 cups

flour does he need to make the dough,

=41/4-9/2

=(41-18)/4

=23/4

=5 3/4 cups

He needs 5 3/4 cups of floor to make the dough.

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The value of a4 would be equal to -666.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that [tex]a_0=10[/tex] and [tex]a_n+1=-5a_n[/tex]

This is a recursive formula. So we can simply substitute in each value. For instance, a₂

Use the recursive definition repeatedly.

a2 = -5(6) +4 = -26

 a3 = -5(-26) +4 = 134

 a4 = -5(134) +4 = -666

Therefore, the value of a4 is -666

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For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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The function f(x) = (x - 3)² is invertible on the interval [1,2], as each output is related only with a single input.

The inverse of the function is given as follows:

[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]

The function for this problem is defined as follows:

f(x) = (x - 3)²

The x-coordinate of the vertex of the quadratic function is given as follows:

x = 3.

Hence the function is invertible on the domain [1,2], which is entirely on one side of the vertex, and thus each output is related only with a single input.

The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:

x = (y - 3)²

[tex]y - 3 = -\sqrt{x}[/tex]

[tex]y = -\sqrt{x} - 3[/tex]

[tex]f^{-1}(x) = -\sqrt{x} - 3[/tex]

The negative symbol is because the function is on the left side of the vertex.

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Answer:0, 18, 36, 54, 72, 90, 108, 126, 144, 162

Step-by-step explanation:0 es múltiplo de 18, pues 18 x 0 = 0

18 es múltiplo de 18, pues 18 x 1 = 18

36 es múltiplo de 18, pues 18 x 2 = 36

54 es múltiplo de 18, pues 18 x 3 = 54

72 es múltiplo de 18, pues 18 x 4 = 72

90 es múltiplo de 18, pues 18 x 5 = 90

108 es múltiplo de 18, pues 18 x 6 = 108

126 es múltiplo de 18, pues 18 x 7 = 126

Answer:

Step-by-step explanation:

18: 0, 18, 36, 54, 72, 90, 108, 126, 144, 162

27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270

The function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output.

The vector is a 1-dimensional array. The formula for this function is:

For i = 0 to length-1

   Print ( ptr[i] )

End

The calculation for this function is as follows:

The function starts with a for loop, where the initial value of i is set to 0, and the condition for the for loop is i < length, and the increment value of i is 1. The body of the for loop prints the value of ptr[i], which is the value at the i-th position in the vector. This loop is repeated until the condition i < length is false, at which point the function terminates.

In summary, the function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output. The formula for this function is a for loop, where the initial value of i is set to 0 and the condition for the for loop is i < length. The body of the for loop prints the value of ptr[i], and the loop is repeated until the condition i < length is false.

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The probability that a randomly selected subject in this is Male or answered 'No' is A: 0.18.

The probability that a randomly selected subject in the study is Male or answered "No" is the sum of the probability that the subject is Male and the probability that the subject answered "No", which is a measure of the overlap between these two events.

To find the probability that a subject is Male, we take the number of Male subjects (50) and divide it by the total number of subjects (100):

P(Male) = 50/100 = 0.5

To find the probability that a subject answered "No", we take the number of subjects who answered "No" (48) and divide it by the total number of subjects (100):

P(No) = 48/100 = 0.48

We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected subject is Male or answered "No"

P(Male or No) = P(Male) + P(No) - P(Male and No)

We know that 18 out of 50 Male subjects answered No and 16 out of 50 Female subjects answered no, so the probability that a Male subject answered No is 18/50 = 0.36, and the probability that a Female subject answered No is 16/50 = 0.32

P(Male and No) = P(Male) * P(No|Male) = 0.5 * 0.36 = 0.18

P(Female and No) = P(Female) * P(No|Female) = 0

Hence, the probability that a randomly chosen subject in this is male or answered 'no' is A: 0.18.

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The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number.

The set of all points in an open subset of the complex plane, such that the absolute value of a given continuous function is equal to a given number, is a set of points that can be found by taking the given continuous function and evaluating it at each point in the open subset of the complex plane. This set of points can be expressed as a set of the form [tex]$\{z \in u: |f(z)|=c\}$[/tex] where u is the open subset of the complex plane and f  is the given continuous function. The absolute value of the function must be equal to some number c in order for the point to be included in the set. This set of points is useful for understanding the behavior and properties of the given continuous function on the open subset of the complex plane.

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a. Taxpayer having a taxable income of $39,800 has $5,448 as the income tax.

b. The taxable income of taxpayer owing $21,197 is $102,800.

What is Income Tax?

Income tax is the tax which is levied on all individuals and businesses. The individual income taxes are calculated on the basis of the income received by the individual. Typically, it is categorized as a direct tax because the burden is thought to fall on the people who pay it. Net profits, calculated as the excess of receipts over permitted costs, are subject to corporate income tax.

We are given graph of a piecewise function with three equations which is attached below.

From the graph, it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.

Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.

His taxable income is $102,800 as shown in the graph  below.

Hence, taxpayer having a taxable income of $39,800 has $5,448 as the income tax and the taxable income of taxpayer owing $21,197 is $102,800.

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Answer:

1 1 1 1 to base two

Step-by-step explanation:

1 0 1 base two

× 1 1 base two

+ 1 0 1

1 0 1

=1 1 1 1 base two

Correct option is C, The information about the acids that are created from the sugar in sweets and bacteria from teeth comes from Jaws.

gum, lollipops, and hard sweets without additional sugar.

Gum with a high Xylitol content, like Icebreaker Ice Cubes, makes you salivate more, which helps kill dangerous bacteria. Hard sweets and sugar-free lollipops can also stimulate the salivary glands.

Black chocolate offers more antioxidants than milk chocolate and less sugar.

As long as it is eaten in moderation and leaves your teeth bushed, the occasional candy piece is acceptable.

The greatest strategy to stop sugar's harmful effects on teeth is to always pay close attention. We advise you to limit your sugar intake, regularly brush away the bacteria-filled plaque on your teeth, and consume nutritional meals to maintain strong teeth.

Combining routine dental exams with fluoride treatments from our dental team will give you and your family the best chance of preventing tooth decay.

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1.33 cm/s

Step-by-step explanation:

The line is going from point (0;0) to point (12;16), the proportional relationship between these points refer to the slope of the line, which can be found with this expression:

Replacing all values we have:

Therefore the relation shown in the graph is represented by 1.33 cm/s, which refers to the constant speed developed by the object.

Is this what your looking for if not let me know

Answer:

1.33 cm/s

Step-by-step explanation: