Answer:
Step-by-step explanation:
// Solve equation [2] for the variable x
[2] x = y + 1
// Plug this in for variable x in equation [1]
[1] (y +1) - 2y = 9
[1] - y = 8
// Solve equation [1] for the variable y
[1] y = - 8
// By now we know this much :
x = y+1
y = -8
// Use the y value to solve for x
x = (-8)+1 = -7
Solution :
{x,y} = {-7,-8}
A rectangular prism is 6 centimeters long and 16 centimeters high. Its volume is 1,152 cubic centimeters. What is the width of the rectangular prism?
The width of the rectangular prism as required to be determined is 12 centimetres.
What is the measure of the prism's width?As evident in the task content; the rectangular prism is 6 centimeters long and 16 centimeters high while Its volume is 1,152 cubic centimeters.
Since for rectangular prisms;
Volume = length × width × height
Where,
Length = 6 centimeters
Width = w
Height = 16 centimeters
So,
Volume = length × width × height
1152 = 6 × w × 16
w = 1152 / 96
w = 12 centimeters
Ultimately the width of the rectangular prism in discuss is;12 centimetres.
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Rewrite the logarithmic expression as a single logarithm with the same base. Assume all expressions exist and are well-defined. Simplify any fractions. 9log_(4)2-log_(4)40
The logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex].
To rewrite the logarithmic expression as a single logarithm with the same base means that we have to do logarithmic expression simplification.
To do so, we can use the logarithmic properties:
[tex]log_{b} (a)[/tex] + [tex]log_{b} (c)[/tex] = [tex]log_{b} (ac)[/tex]
[tex]log_{b} (a)[/tex] - [tex]log_{b} (c)[/tex] = [tex]log_{b} (a/c)[/tex]
b · [tex]log_{a} (x)[/tex] = [tex]log_{a} (x^{b} )[/tex]
Using these properties, we can rewrite the given expression:
9 · [tex]log_{4} (2)[/tex] - [tex]log_{4} (40)[/tex] = [tex]log_{4} (2^{9} )[/tex] - [tex]log_{4} (40)[/tex]
= [tex]log_{4} (512)[/tex] - [tex]log_{4} (40)[/tex]
= [tex]log_{4} (512/40)[/tex]
= [tex]log_{4} (12.8)[/tex]
So the logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex]
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Jim Brown bought a house with a 11. 5% adjustable rate mortgage for 20 years. He was paying $10. 67 monthly per thousand on his original loan. At the end of 4 years he owes the bank $70,000. Interest has now gone up to 13%, the bank can renew the mortgage at this rate or Jim can pay the full $70,000. Jim renews the mortgage and will pay $11. 72 monthly per thousand on this loan.
What is the amount of the old monthly payment, new monthly payment, and the percentage increase of the new monthly payment?
old monthly payment = $
new monthly payment = $
% increase
The percentage increase in the new monthly payment is a 35.5% decrease compared to the old monthly payment.
What are percentages?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
The original monthly payment per thousand dollars of the loan is $10.67. So, for a loan amount of x dollars, the original monthly payment can be written as:
10.67 x (x/1000) = 0.01067x
The term (x/1000) is used to convert the loan amount from dollars to thousands of dollars.
Jim has been paying this monthly payment for 4 years or 48 months. So, the total amount he has paid towards the loan is:
48 x 0.01067x = 0.51216x
At the end of 4 years, Jim owes the bank $70,000. So, we can write:
x - 0.51216x = 70000
0.48784x = 70000
x = 143391.99 (rounded to the nearest cent)
Now, we can use the new interest rate and monthly payment information to find the new monthly payment.
The new monthly payment per thousand dollars of the loan is $11.72. So, for a loan amount of x dollars, the new monthly payment can be written as:
11.72 x (x/1000) = 0.01172x
The new interest rate is 13%, which is applied to the remaining loan amount of $70,000. So, the new loan amount can be written as:
0.13 x 70000 + 70000 = 79100
Therefore, the new monthly payment for the loan amount of $79,100 is:
0.01172 x 79100 = $927.11 (rounded to the nearest cent)
To find the percentage increase in the new monthly payment, we can use the formula:
% increase = (new value - old value) / old value x 100
% increase = (927.11 - 1437.32) / 1437.32 x 100
% increase = -35.5%
Therefore, the percentage increase in the new monthly payment is a 35.5% decrease compared to the old monthly payment.
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If the matrix A = [a1 a2 a3 a4 a5]
has reduced row echelon form
[ 1 -1 0 0 2 ]
[ 0 0 1 0 3 ]
[ 0 0 0 1 1 ]
[ 0 0 0 0 0 ]
then a basis for Col(A) is [ __ __ __ ].
(Note that a1, a2, a3, a4 and a5 are t
If the matrix A = [a1 a2 a3 a4 a5] has reduced row echelon form [1−102][00031][00001][00000], then a basis for Col(A) is [a1−a2a3a4].
Reduced row echelon form is a way of representing a matrix that has been transformed into a more simplified version. It is commonly used in linear algebra and has many applications.
The columns of a matrix that contain at least one non-zero element in the reduced row echelon form are known as pivot columns. Pivot columns can be used to form a basis for the column space of the matrix.
The number of pivot columns determines the rank of the matrix. Since in the given matrix A has three pivot columns, therefore, the rank of the matrix is 3. Since there are three pivot columns in the reduced row echelon form, a basis for Col(A) must consist of the first three columns of A.
Hence, the required basis for Col(A) is [a1−a2a3a4].
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8900 dollars is placed in a savings account with an annual interest rate of 3.3% if no money is added or removed from the account which equation represents how much will be in the account after 4 years
Answer: 10134.2425
Step-by-step explanation:
Your initial number, 8900, is multiplied by 1+.033 because your percent and your adding money. It all is then raised to the power of 4. Your equation will be 8900(1+.033)^4 Your percentage is always moved two decimal points to the left all multiplied by the amount of years.
How many entities are depicted by the following requirements? School XYZ keeps track of its 100 students, 10 teachers, and 5 classrooms. A) 3 B) 4 C) 115 D) 116
The total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.
What is the algebraic operation?
An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
The question asks us to determine the number of entities depicted by the given requirements, which include School XYZ keeping track of its 100 students, 10 teachers, and 5 classrooms.
An entity can be defined as a distinct object or concept that is represented in a system, such as a database or software application.
In this case, the entities can be identified as follows:
Students: There are 100 students in the school, and each student can be considered as a separate entity.
Teachers: There are 10 teachers in the school, and each teacher can be considered as a separate entity.
Classrooms: There are 5 classrooms in the school, and each classroom can be considered separate.
Therefore, the total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.
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Escribir la ecuación cuadrática con raíces 1 y 5, y con coeficiente principal 2.
(Utilizar la letra x para representar la variable. )
The quadratic equation with roots 1 and 5 and leading coefficient 2 is 2x^2 - 12x + 10 = 0
To write the quadratic equation with roots 1 and 5 and leading coefficient 2, we can use the fact that the general form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are constants.
Since the roots are 1 and 5, we know that the factors of the quadratic equation are:
(x - 1) and (x - 5)
Multiplying these factors together, we get:
(x - 1)(x - 5) = x^2 - 6x + 5
To satisfy the condition of having a leading coefficient of 2, we can simply multiply the entire equation by 2
2(x^2 - 6x + 5) = 2x^2 - 12x + 10
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OAB is a sector of a circle as shown below.
Work out the length of the arc AB.
Give your answer in millimetres (mm) to
1 d.p.
IMPORTANT
The length of the arc AB is 44.7 mm
What is the length of an arc?A sector is a part of a given circle which is bounded by two radii and an arc. The length of an arc is simply the path of the incomplete circle.
The length of an arc can be determined by:
length of an arc = θ/ 360 2πr
Where is the measure of the central angle, and r is the radius of the circle.
From the diagram given,
The length of arc AB = θ/ 360 2πr
= 61/ 360*2*22/7*42
= 44.7333
The length of arc AB is 44.7 mm.
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Which Value Of X Will Make The Expression?
Answer:
2 and -2
Step-by-step explanation:
For the expression to be equal to 0, it means it has to be undefined, so all we need do, is equate the denominator to 0, since any number divided by 0 = 0
Therefore,
5x² - 20 = 0
5x² = 0 + 20
5x² = 20
Divide both sides by 5,
x² = 20/5
x² = 4
Square root both sides,
x² = √4
x = ±2
Please mark brainliest.
Thanks.
Which of the following gives the correct range for the graph? −2 ≤ x ≤ 5
For the functiοn, the range is deduced tο be [-2, 5].
What is the range of data?
The range οf data is defined as a measure of the difference between the maximum value of data and the minimum value οf data.
The rangeοf a graph refers to the set of all possible output values, or the y-values, οf the function represented by the graph.
The given range of −2 ≤ x ≤ 5 actually represents the domain of the function, or the set οf all possible input values, or the x-values, fοr which the function is defined.
Sο, the range can also be written as [-2, 5] for the given set of data.
Therefore, the range is οbtained as [-2, 5].
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What is the variable in the equation? x + 2 = 8
O Х
O 2
O +
O =
The variable in the equation? x + 2 = 8 is 'x'.
What is Expression?An expression is a grouping of terms that have been joined together using mathematical operations such as subtraction, addition, multiplication, and division. In mathematics, the terms involved in an expression are:
A constant is an unchanging numerical value.Variable: A variable is a symbol with no fixed value.A term might be a single constant, a single variable, or a combination of a variable and a constant multiplied or divided.A coefficient is a number in an equation that is multiplied by a variable.We have the Equation: x+ 2 = 8.
as, we know that Equation is the combination of variables, Operation, numbers and Equal Sign,
So, the variable is x
and, Number is 8
and, Operation is +
Thus, the Variable in equation is x.
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I need help ASAP! What is the expanded form of this number
15.306
A. (1 x 10) + (5 x 1) + (3 x 1/10) + (6 x 1/1000)
B. (1×10) + (5×1) + (3×110) + (6× 1/1000)
C. (1×10) + (5×1) + (3×1/100) +(6×1/100)
D. (1×10) + (5×1) + (3×1/100) + (6×1/1,000)
Answer:
the answer is A
So basically it's simple just use some scientific calculator and put the number one by one with the bracket because there's a rule of mathematics which we call BODMAS
Please please help me! This is due ASAP
sin 200 degrees cos 80 degrees- cos 200 degrees sin 80 degrees
Thank you!!
Answer:
0.866
Step-by-step explanation:
sin (200) = −0.34202014
cos (80) = 0.17364817
-
cos (200) = −0.93969262
sin (80) = 0.98480775
=
0.86602540338, or 0.866
Suppose a Stand Alone Senior High School plans to assign the identification numbers of their students into eight-digit number such that no digit is to be used more than once in any ID number. How many ID numbers can be made out of 0,1,2,3,4,5,6,7,8, and 9?
The number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3265920.
To find the number of ID numbers that can be made, we can use the permutation formula:
P(n,r) = n! / (n-r)!
Where n is the total number of digits available and r is the number of digits in the ID number.
In this case, n = 10 (the digits 0-9) and r = 8 (the number of digits in the ID number).
Plugging these values into the formula gives us:
P(10,8) = 10! / (10-8)!
P(10,8) = 10! / 2!
P(10,8) = 3628800 / 2
P(10,8) = 1814400
However, we need to subtract the number of ID numbers that start with 0, since these would not be valid eight-digit numbers. To find this number, we can use the permutation formula again with n = 9 (the digits 1-9) and r = 7 (the remaining digits in the ID number):
P(9,7) = 9! / (9-7)!
P(9,7) = 9! / 2!
P(9,7) = 362880 / 2
P(9,7) = 181440
Subtracting this from the total number of ID numbers gives us:
3265920 - 181440 = 3084480
So the number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3084480.
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Solve 2 sin^2 (x) – sin(x) – 1=0 for all solutions 0 < x < 2π
X = _____
Give your answers as a list separated by commas
The solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:
X = π/2, 11π/6
To solve the equation 2 sin^2 (x) – sin(x) – 1=0 for all solutions 0 < x < 2π, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -1, and c = -1. Plugging these values into the quadratic formula gives us:
x = (-(-1) ± √((-1)^2 - 4(2)(-1))) / (2(2))
Simplifying the expression inside the square root gives us:
x = (1 ± √(1 + 8)) / 4
x = (1 ± √9) / 4
x = (1 ± 3) / 4
This gives us two possible values for x:
x = (1 + 3) / 4 = 1
x = (1 - 3) / 4 = -0.5
Now we need to find the values of x that satisfy the original equation and are within the given range of 0 < x < 2π. To do this, we can use the inverse sine function:
x = sin^-1(1) = π/2
x = sin^-1(-0.5) = -π/6
Since we are looking for solutions within the range of 0 < x < 2π, we need to add 2π to the nagetive solution to get a positive value:
x = -π/6 + 2π = 11π/6
Therefore, the solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:
X = π/2, 11π/6
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HELP ASAP PLSSSSS
Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 60
Age 15 and above 65 195
Column totals 152 110 98 360
How many students age 15 and above take a car to school?
18
38
50
87
The correct option is (b) i.e. there are 38 students age 15 and above who take a car to school.
What is a linear equation?
A linear equation is one in which the maximum power of the variable is one. Mathematically, an equation of the type axe + b = 0 or axe + by + c = 0, where a, b, and c are real integers and x and y are variables of maximum power one.
We know that,
Students under age 15 who prefer walk/bike + Students age 15 and above who prefer walk/bike = total of column
So, Students under age 15 who prefer walk/bike
= total of column - Students age 15 and above who prefer walk/bike
= 152 - 65
= 87.
Now, total of rows = total of columns
Row 1 + Row 2 = 360
Row 1 = 360 - Row 2
=360-195
= 165.
Now, Students under age 15 who prefer bus + Students under age 15 who prefer walk/bike + Students under age 15 who prefer car = Row table
So, Students under age 15 who prefer bus
= 165 - 60 - 87
= 18.
Similarly,
Students under age 15 who prefer bus + Students 15 and above who prefer bus = column total
So, Students 15 and above who prefer bus = 110 - 18
= 92.
Finally, students age 15 and above take a car to school
= 195 - 92 - 65
= 38.
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The average female blue whale has a length of 82 feet. If you are creating a model with a scale of 1 inch=4 feet, how long will the model be?
Answer:
20.5 in.
Step-by-step explanation:
Just divide 82 by 4 to get the answer since 1 inch equals to 4 feet.
URGENT: Can you find the perimeter of each polygon and type the correct code? Please remember to type in ALL CAPS with no spaces.
PLEASEEEE HELPPP NOW!!!
Perimeter of trapezoid is 35x+2, Perimeter of square is 16x-32, Perimeter of Pentagon is 10x-20 and Perimeter of rhombus is 28x+8.
What is Polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
Perimeter of trapezoid=9x+4+7x+8+12x-2+7x-8
Add the like terms
35x+2
Perimeter of trapezoid is 35x+2
Perimeter of square= 4(4x-8)
=16x-32
Perimeter of Pentagon=5(2x-4)
=10x-20
Perimeter of rhombus=4(7x+2)
=28x+8
Hence, Perimeter of trapezoid is 35x+2, Perimeter of square is 16x-32, Perimeter of Pentagon is 10x-20 and Perimeter of rhombus is 28x+8.
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On a road, a bike sign in the shape of an isosceles trapezoid is to be painted. The sign and its dimensions are shown below. What is the area of the sign?
A right trapezoid is shown with a height labeled 5 feet and one of the bases labeled as 8 feet, and the other base is labeled as 6 feet.
(5 points)
a
30 square feet
b
35 square feet
c
45 square feet
d
50 square feet
The area of the sign is 35 square feet. The solution has been obtained by using the area of the trapezoid.
What is area of the trapezoid?The entire area occupied by the sides of a trapezoid is its area. A trapezoid's area is determined by how many unit squares fit inside of it.
We know that area of the trapezoid is
Area (A) = (a + b ) * h/ 2
Now, here we are given the following:
a = 8
b = 6
h = 5
Now, on substituting these values in the formula, we get
⇒A = (8 + 6 ) * 5 / 2
⇒A = (14 * 5) / 2
⇒A = 70 / 2
⇒A = 35 square feet
Hence, the area of the sign is 35 square feet.
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descripition of Ff ?
When ff. is written it refers to the page or line mentioned and two or more pages or lines after it or a set of numbers as a function.
What is set?
A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter.
According to set theory, a set's constituent parts can be anything, including humans, alphabetic letters, numbers, shapes, variables, etc.
The types of set are:
Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.
Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}
Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}
Equal Set: Two sets that have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B
Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B
Universal Set: A set that consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}
Hence, ff(x) means that you have to replace x with f(x) in f(x).
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Jayden made 5% of his free throws over the season. If he shot 120 free throws, how many did he make? Divide/scale down to solve for the missing percent.
Answer:6
Step-by-step explanation:If jayden made 5% of his free throws and he shot 120 free throws you have to find 5% of 120.
5% of 120 = 6
So Jayden shot a total of 6 free throws during the season
when Aaron runs the 400 m dash is finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2.5 seconds using the elliptical rule determine the interval of times that represent the middle 99.7% of his finishing times in the 400 m race.
So, by resolving the given, we obtain the result: As a result, the range of standard deviation timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.
What is standard deviation?A statistic called standard deviation may be used to represent the variability or variation of a collection of statistics. A low standard deviation means that the values often tend to be closer to the set mean, whereas a large standard deviation shows that the values are widely spread. The standard deviation is an indicator of how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is small, and are more scattered when it is big. Standard deviation is the average degree of variability in the data collection. It displays each score's standard deviation from the mean.
We can thus get the z-scores that correspond to the bottom and upper bounds of this range using the z-score calculation formula:
Lower bound: z = (x - )/z = (x - 80)/z = 2.5 z = -3
The maximum value is z = (x - ) / z = (x - 80) / 2.5 z = 3.
The area under the curve between z = -3 and z = 3 can be calculated using a calculator or a conventional normal distribution table.
The minimum value is z = -3 (x - 80) / 2.5 = -3 x - 80 = -7.5 x = 72.5.
z = 3 (x - 80) / 2.5 = 3 x - 80 = 7.5 x = 87.5 is the upper limit.
As a result, the range of timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.
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Consider the set of vectors x, x + 3x^2, x^3, x^2 ∈ P[x]. Does
this set span P[x]?
No, the set of vectors x, x + 3x², x³, x² does not span P[x].
To span P[x], a set of vectors must be able to generate any polynomial in P[x] through a linear combination of the vectors in the set. However, the set given only includes polynomials of degree 1, 2, and 3. This means that it cannot generate polynomials of degree 0 (constants) or polynomials of degree 4 or higher.
For example, the polynomial 5 cannot be generated from a linear combination of the vectors in the set, as there are no constants in the set. Similarly, the polynomial x⁴ cannot be generated, as there are no vectors of degree 4 or higher in the set.
Therefore, the set of vectors x, x + 3x², x³, x² does not span P[x].
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Please help, I don't know how to do this!!!
the height of the antenna is approximately 24 meters.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
From the diagram, we see that we need to find the distance d and the height h. We can use the tangent function to find these values.
First, let's find d:
tan(θ) = h / (d + 1.51)
Rearranging, we get:
d = (h / tan(θ)) - 1.51
Next, let's find h:
tan(θ') = h / d
Substituting the expression for d that we found above, we get:
tan(θ') = h / ((h / tan(θ)) - 1.51)
Multiplying both sides by (h/tan(θ1)) - 1.51 and simplifying, we get:
h = (29 * tan(θ') * tan(θ)) / (tan(θ') - tan(θ))
Now we can plug in the values for the angles and solve for h:
h = (29 * tan(31°) * tan(17°)) / (tan(31°) - tan(17°))
h ≈ 24
So the height of the antenna is approximately 24 meters.
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Hi! Please help! question attached tysm x
so the rate is per annum, so compounding period is 1 per year, hmmm we could use 1 or 2 years to get "r", hmmm let's use 2.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 5903.13\\ P=\textit{original amount deposited}\dotfill &\pounds 5500\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]
[tex]5903.13 = 5500\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 2} \implies \cfrac{5903.13}{5500}=\left( 1+\cfrac{r}{100} \right)^2 \\\\\\ \sqrt{\cfrac{5903.13}{5500}}=\cfrac{100+r}{100}\implies 100\sqrt{\cfrac{5903.13}{5500}}=100+r \\\\\\ 100\sqrt{\cfrac{5903.13}{5500}}-100=r\implies \stackrel{ \% ~ ~~ ~ }{\boxed{3.6\approx r}}[/tex]
Nolan was studying birth weights of infants in Somalia. He took an SRS (simple random sample) of 100 births and calculated a sample mean birth
weight of & = 3.2 kg. The sample data was slightly skewed with a few
outliers. He is considering using his data to construct a confidence interval for the mean birth weight in Somalia.
Which conditions for constructing at interval have been met?
It appears that Nolan has met the conditions for constructing a confidence interval for the mean birth weight in Somalia. However, he should also check the skewness and presence of outliers in the sample to ensure that the normal approximation is appropriate.
What is skewed data?In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.
Start-up effects can also cause skewness.
To construct a confidence interval for the mean birth weight in Somalia, we need to ensure that the following conditions are met:
Random Sampling: Nolan used a simple random sample of 100 births, which meets the condition of random sampling.
Independence: Each birth weight in the sample should be independent of the other. This condition is met if the sample size is less than 10% of the total population of births in Somalia.
Sample size: In general, a sample size of at least 30 is recommended to use the normal distribution to approximate the sampling distribution of the sample mean. Since Nolan's sample size is 100, this condition is met.
Skewness and outliers: Nolan mentioned that the sample data was slightly skewed with a few outliers.
Therefore, all the required conditions are given above.
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Answer:
the data is a random sample from the population of interest.
the sampling distribution of x is approximately normal.
individual observations can be considered independent.
Step-by-step explanation:
The tourist walked x hours with a speed of 5 kilometers per hour and y hours with a speed of 4 kilometers per hour. Write an equation expressed with x and y to find the tourist's average speed over the whole distance he walked.
The equation expressed with x and y to find the tourist's average speed over the whole distance he walked is (5x + 4y) / (x + y)
What is the average speed?Average speed = Total distance traveled / Total time taken
Distance = speed × time
= 5 km/h × x
= 5x km/h
Distance = speed × time
= 4 km/h × y
= 4y km/h
Average speed = Total distance traveled / Total time taken
= (5x + 4y) / (x + y)
Therefore, the tourist's average speed over the whole distance he walked is represented by (5x + 4y) / (x + y)
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what is the quotient to 5984 divided by 32
Answer:
The quotient of 5984 divided by 32 is 187.5
Step-by-step explanation:
Answer:
The quotient of 5984 divided by 32 is 187.
Find the equation for the line that passes through the point
(2,0) , and that is perpendicular to the line with the equation
y−4=−13(x+3) .
The equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] is [tex]x - 13y = 2.[/tex]
To find the equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] we need to find the slope of the perpendicular line and use the point-slope form of the equation of a line.
Step 1: Find the slope of the given line.
The equation of the given line is[tex]y-4=-13(x+3)[/tex]. This is in the form [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line. Therefore, the slope of the given line is -13.
Step 2: Find the slope of the perpendicular line.
The slope of two perpendicular lines are negative reciprocals of each other. So, the slope of the perpendicular line is 1/13.
Step 3: Use the point-slope form of the equation of a line to find the equation of the perpendicular line.
The point-slope form of the equation of a line is [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line and [tex](x1, y1)[/tex] is a point on the line. Substituting the values of the slope and the point into the equation, we get:
[tex]y - 0 = (1/13)(x - 2)[/tex]
[tex]y = (1/13)x - (2/13)[/tex]
Step 4: Simplify the equation.
Multiplying both sides of the equation by 13, we get:
[tex]13y = x - 2[/tex]
Step 5: Rearrange the equation to get the standard form of the equation of a line.
The standard form of the equation of a line is Ax + By = C, where A, B, and C are constants. Rearranging the equation, we get:
[tex]x - 13y = 2[/tex]
Therefore, the equation of the line that passes through the point (2,0) and is perpendicular to the line[tex]y-4=-13(x+3)[/tex] is x - [tex]13y = 2[/tex].
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Compare the graph of g(x) = 3x2 + 6 with the graph of f(x) = x2.
The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.
However, they have different coefficients and constant terms, which means that they will have different shapes and positions.
Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².
Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.
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