The lowest values of x are;
1. x = 1/2, x = 2/4, x = 3/6
2. x = 14, 15, 16
How to determine the valuesFrom the information given, we have that;
10-3x > 8
collect the like terms, we get;
-3x > 8 - 10
subtract the values
-3x > -2
Make 'x' the subject
x > 2/3
5x-27 > 7x
collect the like terms
5x - 7x> 27
subtract the like terms
-2x> 27
Make 'x' the subject
x > -27/2
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Describe a single transformation of △ABC that is a composition of the following pair of transformations:
T<−5,−3>(ABC) followed by T<−4,−2> (A'B'C).
A. T<−1,−5>(ABC)
B. T<−9,−5>(ABC)
C. T<−9,−1>(ABC)
D. T<−1,−1>(ABC)
The required overall translation is T<−9,−5>(ABC). The correct answer would be option B.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Starting with triangle ABC, we first apply the transformation T<−5,−3>, which means each vertex of the triangle is shifted 5 units to the left and 3 units down. So the triangle becomes A'B'C'.
Next, we apply the transformation T<−4,−2> to triangle A'B'C', meaning that each vertex is shifted 4 units to the left and 2 units down.
To find the overall effect of these two transformations, we can think of the second transformation as shifting the entire triangle produced by the first transformation.
In other words, we're combining the effects of the two transformations by adding the translations together.
So, the overall translation is T<−5 + −4, −3 + −2> = T<−9,−5>,
Thus, the correct answer would be option B: T<−9,−5>(ABC).
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What is 22/22X22-22+22? Then 33/33X33-33+33? Then Divide both answers by 5?
Answer:
22/22X22-22+22= 22÷5 =4.5
33/33X33-33+33=33÷5=6.6
A verbal description of a linear function h is given. Express the function h in the form
h(x) = ax + b.
The graph of the linear function h has slope
8
9
and y-intercept 3.
h(x) =
The graph of the linear function h has slope the function h in the form
h(x) = 8x + 9.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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If you borrow $1,100 for
9 years at an annual
interest rate of 4%,
what is the total
amount of money you
will pay back?
The amount of interest paid will be $396.6.
What is simple interest?The simple interest is the simple amount paid by the borrower to the bank according to the percentage set by the bank for per year which is a fixed interest rate.
Given that Margo takes out a $600 loan with a 10-month repayment period and a 2% yearly interest rate.
The simple interest will be calculated as:-
SI = ( P x R x T ) / 100
SI = ( 1100 x 9 x 4 ) / 100
SI = 39600 / 100
SI = $396
Therefore, $396 will be paid in interest.
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The mail carrier has to deliver three boxes The first Box has the mass of 80 kg the second Box has the mass of 40 kgs third box has a mass of 60 kg what is the total mass of all three boxes in grams?
The total mass of all three boxes to be delivered by the mail carrier is 180,000 grams.
What is the total mass of all three boxes in grams?Given the data in the question;
Mass of the boxes carried by the mail carrier.
Mass of first box = 80kg
Mass of second box = 40kg
Mass of third box = 60kg
First, we convert from kilograms to grams.
Note: 1 kg = 1000g
Hence;
Mass of first box = 80kg = ( 80 × 1000 )g = 80000g
Mass of second box = 40kg = ( 40 × 1000 )g = 40000g
Mass of third box = 60kg = ( 60 × 1000 )g = 60000g
Now, we add the mass of the boxes in gram.
80000g + 40000g + 60000g
180,000 grams
Therefore, the total mass is 180,000 grams.
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Consider a political discussion group consisting of 6 Democrats, 4 Republicans, and 6 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting and then .
The probability of selecting a Democrat and then an Independent is (6/16) * (6/15) = 3/40. The probability of selecting two Republicans with replacement is (4/16) * (4/16) = 1/16.
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. It is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given situation. Probability is used in many fields, such as mathematics, statistics, science, engineering, economics, and social sciences, to model and analyze uncertain situations and make predictions about the future based on available data.
(a) selecting a Democrat and then an Independent without replacement.
The probability of selecting a Democrat on the first draw is 6/16, and the probability of selecting an Independent on the second draw, without replacement, is 6/15. So the probability of selecting a Democrat and then an Independent is:
(6/16) * (6/15) = 3/40
(b) selecting two Republicans with replacement.
The probability of selecting a Republican on the first draw is 4/16, and with replacement, the probability of selecting another Republican on the second draw is also 4/16. So the probability of selecting two Republicans with replacement is:
(4/16) * (4/16) = 1/16
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Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and let y be the number of meters Tarzan is from the riverbank. Assume that y varies sinusoidally with t, and that y is positive when Tarzan is over water and negative when he is over land. Jane finds that when t = 2, Tarzan is at one end of his swing, where y = -23. She finds when t = 5 he reaches the other end of his swing and y = 17.
We can represent the sinusoidal function for Tarzan's motion as given below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch.
Assume the sinusoidal equation to be -
y = Asin(ωt)
We can represent the coordinates as -
For {t} = 2, {y} = -23. So -
- 23 = Asin(2ω) ... { 1 }
For {t} = 5, {y} = 17. So -
17 = Asin(5ω) ... { 2 }
Therefore, we can represent the sinusoidal function for Tarzan's motion as given above.
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Find the second and fifth term of 3n(squared)-1
Trapezoid WXYZ is rotated about its center and then translated down and to the right to produce trapezoid h j KL the side WZ is 7 cm WX is 5 cm y z is 5 cm and XY is 9 cm how long is side LH
The length of side LH is given as follows:
LH = 7 cm.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
This is relevant because the side lengths remain constant.
The equivalent side to side LH is given as follows:
WZ = 7 cm.
Hence the length of side LH is given as follows:
LH = 7 cm.
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o TP & E Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. X = y = Z= - 3x + - 2x + y 4y 4y + - 2z = -8 7z = 26 8z = 30 Question Help: Video 1 Video 2 M Message instructor
The system of equations can be written as a matrix and then used to solve for the variables x, y, and z.
The augmented matrix of the system is:
-3 -2 1 | -8
0 4 -2 | -8
0 0 7 | 26
We can use row operations to find the row reduced echelon form of the matrix, which will give us the solutions to the system.
Starting with the first row:
1. Multiply row 1 by -3 to get a leading 1 in the first column:
3 6 -3 | 24
0 4 -2 | -8
0 0 7 | 26
2. Add row 1 to row 2:
3 6 -3 | 24
0 4 0 | 16
0 0 7 | 26
3. Add 3 times row 1 to row 3:
3 6 -3 | 24
0 4 0 | 16
0 0 7 | 26
The row reduced echelon form of the matrix is:
1 2 -1 | 8
0 1 0 | 4
0 0 1 | 9
From this, we can see that the solutions to the system are:
x = 8 - 2y
y = 4
z = 9
So the system has a unique solution: x = 8 - 2y = 8 - 2 * 4 = 0, y = 4, z = 9.
Please help me find the answer!!!
Answer:
270 square units
Step-by-step explanation:
The area of a regular hexagon is given by the equation:
A = (1/2)(a · P)
where a is the hexagon's apothem and P is its perimeter.
1. We can first solve for the hexagon's perimeter by multiplying its side length (given as 15) by 6, since there are 6 sides.
P = 15 · 6 = 90
2. Now, we can plug that perimeter value into the formula for the area of a regular hexagon (above).
A = (1/2)(90 · 6)
A = (1/2)(540)
A = 270 square units
Which number is the larger one in the decimal system?
3 x 102 or 1100
F(-10)=64 and f(15)=54
What is the slope
Equation and x intercept
The equation of the straight line is 2x+5y=340.
The x-intercept point of that line is (170,0).
What is the equation of a straight line?A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.
here, we have,
As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).
Now, use the two-point form of the equation of a line.
(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)
(y-64)/(x-(-10))=(54-64)/(15-(-10))
(y-64)/(x-10)=-10/25
25(y-64)=-10(x-10)
5(y-64)=-2(x-10)
5y-320=-2x+20
2x+5y=340
Therefore, the required equation of the line is 2x+5y=340.
To find the x-intercept, substitute y=0 into the equation of the line.
2x+5×0=340
2x=340
x=170
Therefore, the x-intercept point is (170,0).
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Mr. Harrison is going to offer tutoring after school. He is going to charge each student a $35 fee and then $15.50 per hour of tutoring. Which equation represents the total cost for each student to attend Mr. Harrison's tutoring session, if the student spend x number of hours in tutoring.
The student spends x hours tutoring, so y = 15.50x + 35, where x is the number of hours of tutoring and y is the total cost. Therefore, the total cost for a student who receives tutoring for two hours is $66.
What do you mean by tutoring?According to the dictionary definition, a tutor is a person who provides one-on-one or occasionally small-group teaching. The goal of tutoring is to enable students to help themselves, or to support or mentor them until they reach the point at which they are self-sufficient learners and no longer require a tutor.
Tutoring – a teacher's job?Tutors have the ability to, and frequently do, teach students new things. However, when comparing tutoring with teaching, what is being taught is the main difference. Teachers are meant to teach students new content, and tutors teach students how to learn new content.
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Find the value of x that will make L||m
The value of x that will make L||m is 9.
How to find the value of x that will make L||m?
Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life
The angle (4x²- 324)° is equal to 90°. That is:
(4x²- 324)° = 90°
4x²- 324 = 90
4x² = 90 + 324
4x² = 324
x² = 324/4
x² = 81
x = √81
x = 9
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Out of a random sample of 300 voters, it was found that 172 voters are in favor of Issue #1.
Out of a total of 75,000 voters, how many do you predict will vote against Issue #1?
It is predicted that ___
voters are against Issue #1.
A- 30,000
B- 32,000
C- 43,000
D- 60,000
Answer:
B)32000
Step-by-step explanation:
Out of 300, 172 are in favor, and 142/300 is simplfieid as 43/75
43/75 is equal to 43,000/75000
Subtract 75000 by 43000
The difference is 32,000.
32,000 voters are against the Issue.
Colin’s mean mark over three exams was 83%. His mean mark for the first two exams was 76%. What was Colin’s score in the final exam?
Answer: 97%
Step-by-step explanation:
If for the 3 exams, the mean was 83% and the first two were 76%, that means..
76 + 76 = 152 (divided by two = 76%/current mean)
In order to get an average of 83%, Colin has to have a score that is higher than 76% and somewhat closer to above 90%.
By doing trial and error (testing different percents between 76% and 80%), you can come to the conclusion that, 76% + 76% + 97% = 249 / 3 = 83
(5^-4)^2 using only positive exponents
Hi there, here's your answer:
Given the question:
[tex](5^{-4})^{2}[/tex]
We know that a number [tex]x[/tex] raised to the power of a negative integer [tex]-y[/tex] is evaluates as [tex]\frac{1}{x^{y} }[/tex]
Hence, on evaluating this expression we get:
[tex](\frac{1}{5^{4} })^{2}[/tex] = [tex](\frac{1}{625} )^2 = \frac{1}{390625}[/tex]
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The hypotenuse of a right triangle measures 7cm and one of its legs measures 2m. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer: 6.7
Step-by-step explanation: 7^2-2^2=45
square 45 =6.7
Is 4^3.5 halfway between 4^3 and 4^4? If not, explain why. If it is, do you believe that it is
generally true that x^3.5 is halfway between x^3! and x^4? Check out a couple of values to see what you can determine if there is a pattern here. You need to present some
explanation of your observations here.
No, [tex]4^{3}[/tex]. 5 is not equal distance away from both [tex]4^{3}[/tex] and [tex]4^{4}[/tex]. However, when x is a perfect square, it is halfway between [tex]x^{3}[/tex] and [tex]x^{4}[/tex]. 5 is halfway between [tex]9^{3}[/tex] and [tex]9^{4}[/tex].
What is a perfect square?A perfect square is an integer that is the result of multiplying an integer by itself. In other words, it is a number that can be expressed as the product of two equal integers. For example, the number 16 is a perfect square because it can be written as 4 • 4.
Every perfect square has an ending of 1, 4, 5, 6, 9 or 00. (i.e. Even number of zeros). A number that finishes in 2, 3, or 7 is not a perfect square, and so is 8. In essence, a perfect square is the result of multiplying two equal numbers by one another. As a result of multiplying two equal integers (5 and 5) by one another, the number 25 is a perfect square.
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In a large group of students who completed STA 2023, 20% earned an A in the course, 12% didn’t bring their phone to class and 85% of those who didn’t bring their phone to class earned an A
It is given that:
20% of the students earned an A in STA 2023.
12% of the students didn't bring their phones to class.
85% of the students who didn't bring their phones to class earned an A.
To answer the following questions, we assume whether all students took STA 2023 and brought their phones to class or not.
a) Let's assume that x% of the students earned an A and brought their phones to class. Then, since the remaining (100% - 12%) = 88% of students brought their phone to class but their grade is not specified, we can set up the following equation:
x% + 85% of 12% = 20%
x% + 0.102 = 0.20
x% = 0.098
Therefore, 9.8% of students earned an A and brought their phones to class.
b) Let's assume that y% of the students didn't earn an A and didn't bring their phones to class. Then, we can set up the following system of equations:
x% + y% = 100% - 12%
0.85*(12%) = y%
Solving for y, we get:
y% = 9.6%
Therefore, 9.6% of students didn't earn an A and didn't bring their phones to class.
What is STA 2023?STA 2023 is a course code used by some colleges and universities to refer to an introductory course in statistics. The course usually covers topics such as descriptive statistics, probability theory, statistical inference, hypothesis testing, and regression analysis. STA 2023 is often a required course for students majoring in fields such as social sciences, business, and health sciences, as well as for students pursuing degrees in mathematics or statistics. The specific content and level of difficulty of STA 2023 may vary depending on the institution and the instructor.
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9 Mr Karim had 2740 sacks of rice at first Mr Dani had 3560 sacks of rice at first. Mr Karim gave some sacks of rice to Mr Dani. In the end, Mr Dani had 4 times as many sacks of rice as Mr Karim. How many sacks of rice did Mr Karim have in the end?
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
A couch and coffee table cost a total of $1128. The cost of the couch is three times the cost of the coffee table. Find the cost of each item.
cost of couch :
cost of coffee table:
Answer:
cost of couch: $846
cost of coffee table: $282
Step-by-step explanation:
the sides of quadrilateral measure 12cm, 9cm, 16cm, and 20cm.tee longest sides of a similar quadrilateral measure 8cm.find the measure of the remaining sides of a quadrilateral ?
The measure of the remaining sides of a quadrilateral will be 4.8 cm, 3.6 cm, and 6.4 cm.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The sides of the quadrilateral measure 12cm, 9cm, 16cm, and 20cm. The longest sides of a similar quadrilateral measure 8cm. Then the scale factor is given as,
SF = 8 / 20
SF = 0.40
Then the other sides of the quadrilateral are given as,
⇒ 0.40 x 12
⇒ 4.8 cm
⇒ 0.40 x 9
⇒ 3.6 cm
⇒ 0.40 x 16
⇒ 6.4 cm
The measure of the remaining sides of a quadrilateral will be 4.8 cm, 3.6 cm, and 6.4 cm.
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What is the slope between the two points
(-10,50) and (-4,20)
Answer:
Below
Step-by-step explanation:
Slope = rise / run = change in y / change in x = -30 / 6 = -5
Answer: -5
Step-by-step explanation:
Start with the slope formula
m = (y2 - y1) / (x2 - x1)
Substitute point values in the formula
m = (20 - 50) / (-4 - -10)
Simplify the fraction
m = (20 - 50) / (-4 - -10) = -30 / 6
Solve for slope (m)
m = -5
What can be said about the vertices of an equilateral triangle drawn in Poincaré's system?
a. Each of the angles formed at the vertices equals 60 degrees.
b. The vertices are equidistant from the center of the circle.
c. The vertices always lie on the circle.
d. none of these
Please select the best answer from the choices provided
OB
OD
Mark this and return
Next
Submit
Answer:
Step-by-step explanation:
The correct answer is C: The vertices always lie on the circle.
In Poincaré's system, an equilateral triangle is a unique type of triangle in which all three sides are equal in length and all three angles are equal to 60 degrees. Since the vertices of an equilateral triangle lie on the circumference of a circle, it can be said that the vertices always lie on the circle.
The other options, A and B, are also true for equilateral triangles in Poincaré's system, but option C is the best answer because it directly addresses the question of where the vertices lie.
In Poincaré's system, a geometric model of non-Euclidean geometry, the vertices of an equilateral triangle are points that lie on the circumference of a circle.
Here's how this can be demonstrated step by step:
Draw a circle with a center point and a circumference.
Choose three points on the circumference of the circle and connect them with lines to form an equilateral triangle.
Measure the angles at each vertex using a protractor or by counting the number of degrees along the circumference of the circle. In an equilateral triangle, all three angles will be equal to 60 degrees.
Measure the sides of the triangle. In an equilateral triangle, all three sides will be equal in length.
Since the vertices of the triangle are points on the circumference of the circle, it can be concluded that the vertices always lie on the circle.
It is important to note that in Poincaré's system, the relationships between the vertices, sides, and angles of a triangle are different from those in Euclidean geometry. However, an equilateral triangle in Poincaré's system still follows the basic definition of an equilateral triangle, with all sides equal in length and all angles equal to 60 degrees.
There are vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%.
Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
Red
Total
Question content area bottom
Part 1
Complete the table.
Row Relative Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
enter your response here%
enter your response here%
100%
Red
enter your response here%
enter your response here%
100%
Total
enter your response here%
enter your response here%
100%
Answer:
you su ck hah lol
Step-by-step explanation:
ez
A circular walkway is to be built around a monument, with the monument as the center. The distance from the monument to any point on the inner boundary of the walkway is 30 feet.
The equation of the inner boundary of the circular walkway around the monument is x² + y² = 900.
The equation of the outer boundary of the circular walkway around the monument is x² + y² = 1369.
What is the equation of a circle?A circle is a conic section whenever the plane cuts the cone parallel to its base. Every point of the circumference lies at the same distance from its center. The equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
a.
According to the diagram, the radius of the inner boundary is 30 feet and the center is (0, 0).
Substitute h = 0, k = 0, and r = 30 into the equation of circle (x-h)² + (y-k)² = r².
(x-0)² + (y-0)² = 30²
x² + y² = 900
Therefore, the obtained answer is x² + y² = 900.
b.
According to the diagram, the radius of the outer boundary is 37 feet (30 feet + 7 feet) and the center is (0, 0).
Substitute h = 0, k = 0, and r = 37 into the equation of circle (x-h)² + (y-k)² = r².
(x-0)² + (y-0)² = 37²
x² + y² = 1369
Therefore, the obtained answer is x² + y² = 1369.
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The complete question is mentioned in the image below.
A distribution is given as X~ U(0, 12).What is the theoretical mean?
The theoretical mean of the uniform distribution between 0 and 12 is given as follows:
6.
What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The bounds for this problem are given as follows:
a = 0 and b = 12.
As each outcome is equally as likely, the mean of the distribution is equals to the mean of the bounds, hence:
(0 + 12)/2 = 6.
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Ava goes out to lunch. The bill, before tax and tip, was $10. A sales tax of 6% was added on. Ava tipped 24% on the amount after the sales tax was added. How much was the sales tax ? Round to the nearest cent.
Answer:
0.60
Step-by-step explanation:
sales tax=
\,\,\text{6\% of \color{blue}{bill}}
6% of bill
=
=
\,\,0.06\times\color{blue}{\$10}
0.06×$10
6% = 0.06
=
=
\,\,\color{green}{\$0.60}
$0.60
\text{The sales tax was \$0.60.}
The sales tax was $0.60.
