Based on the calculation below, we have:
The tuition per year is $36,000; and
The amount of increase in the tuition each year is $1,000.
How do we calculate tuition and an increase in tuition?The tuition per year and the amount of increase in the tuition each year can be calculated as follows:
Number of semesters in a year = 2
Tuition per semester = $18,000
Amount of increase in the tuition each semester = $500
Therefore, we have:
Tuition per year = Number of semesters in a year * Tuition per semester = 2 * $18,000 = $36,000
Amount of increase in the tuition each year = Number of semesters in a year * Amount of increase in the tuition each semester = 2 * $500 = $1,000
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if p=the mounttain bike's orginal price in dollars, which algebraic expression represents the reduced price ?
Algebraic expression (C) p - 125 represents the reduced price.
What do we mean by algebraic expressions?In mathematics, an algebraic expression is an expression made up of variables and constants as well as algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. Algebraic expressions have at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.So, if p is the mountain bike's original price.
Then, the reduced price will be p - 125.Therefore, algebraic expression (C) p - 125 represents the reduced price.
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Half of the smaller of two consecutive even integers is equal to two more than the larger integer
By solving a linear equation we can see that:
The smaller number is -8The larger number is -6How to find the two numbers?
Here we have two consecutive even integers, we can write these as x and x + 2
We know that half of the smaller of the two is equal to 2 more than the larger one, this can be writen as:
x/2 = (x + 2) + 2
Now we can solve that linear equation for x:
x/2 = x + 2 + 2
x/2 = x + 4
-4 = x - x/2
-4 = x/2
-4*2 = x = -8
The smaller number is -8
The larger number is -8 + 2 = -6
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line A: y = 1/2x + 2
line B: y = -1/2x + 7
line C: y = 2x + 4
line D: y = 1/2x + 5/4
Which lines are perpendicular?
the number in this sequence increase by 40 each time
the sequence is continued with the same rule.
which number in the sequence will be closest to 300
The 8th term of the sequence 310 is closest to the term 300.
What is referred as the arithmetic progression?An arithmetic progression is a series of numbers that have a set common difference in between two consecutive numbers (A.P.).
Each term in an arithmetic sequence increases or decreases by adding or subtracting a constant term.
a = 30 for the first term
d = 40, common difference
We solve in what term is closest to 300 in this manner;
300 / 40 = 7.5
Thus, find the 7th and 8th term.
7th is solved by verifying for;
a₇ = a + ( n - 1 ) d
a₇ = 30 + ( 7 - 1 ) 40
a₇ = 30 + 240
a₇ = 270
The 8th term to certify the closest;
a₈ = T7 + d
a₈ = T7 + 40
a₈ = 270 + 40
a₈ = 310
As a result, the 8th term is the closest, with a value of 310.
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The complete question is-
The numbers in this sequence increase by 40 each time 30, 70, 110,The sequence is continued with the same rule. Which number in the sequence will be closest to 300?
3m / 6 > 3; m = 8 I know the answer is no but can someone explain why???
Answer:
Statement is true
Step-by-step explanation:
3m
---------- > 3; m = 8
6
3(8)
---------- > 3
6
24
---------- > 3
6
24 ÷ 6 = 4
4 > 3
or
3m
---------- > 3; m = 8
6
3m
---------- > 3 (6)
6 (6)
3m > 18
÷3 ÷3
m > 6
8 > 6
Either way, the statement is true. I have no idea why it would be no. I'm sorry if I wasn't of any help.
can you please help me? i also need to know how you got the answer pls and thabk u
Answer:
7 degrees
Step-by-step explanation:
Start with the temperature of -7 deg at 6:00 a.m.
The temperature increases 14 degrees in the next 6 hours.
6 hours after 6:00 a.m. is noon.
We are asked the temperature at noon.
At noon, the temperature is 14 degrees higher than -7 deg.
We add the increase, 14 deg, to the starting temperature, -7 deg.
-7 deg + 14 deg = 7 deg
Answer: 7 degrees
A homeowner whose house was assessed
at $120,000 pays $1,800 in taxes. At the
same rate, what is the tax on a house
assessed at $135,000? PLS SOMEONE HELP me !!!And ty !!!
Thus the tax rate is 1.5% and the 1.5% tax value of $135,000 is $2025.
How do we find the tax rate?We are given that;
A homeowner whose house was assessed at $120,000 pays $1,800 in taxes.
At the same rate, we need to find out what the tax value on a house assessed at $135,000.
The rate is always in percentage. Thus;
Tax value = 5% of 100
= 5/100 x 100
= $5
We have,
House cost = $120,000
Tax amount = $1800.
Let the rate be R%
Now;
R/100 * 120,000 = 1800
R * 1200 = 1800
R = 1800/1200
R = 18/12 = 1.5
R = 1.5%
The tax rate is 1.5%
The 1.5% tax value of $135,000 = 1.5 / 100 * 135,000
= 15/1000 x 135,000
= 15 x 135
= $2025
The tax value is $2025.
Thus the tax rate is 1.5% and the 1.5% tax value of $135,000 is $2025.
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Determine whether each sequence is geometric. If so, find the common ratio. 1/2, 1/4, 1/6, 1/8, . . . . .
The given sequence is not geometric.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: [tex]\frac{1}{2}, \frac{1}{4},\frac{1}{6},\frac{1}{8},...[/tex]
Here, [tex]\frac{\frac{1}{4}}{\frac{1}{2}}\neq \frac{\frac{1}{6}}{\frac{1}{4}}\neq \frac{\frac{1}{8}}{\frac{1}{6}}[/tex]
That is, the given sequence doesn't follow the only required condition for a sequence to be geometric.
Hence, The given sequence is not geometric.
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Supergym is a natural chain of gyms. it's employees sold 5,190 gym memberships last year. this year, they sold 70% more memberships than that. how many memberships did they sell this year?
Super Gym employees sold 8,823 gym memberships this year, 70% more than the 5,190 gym memberships last year.
In mathematics, a percentage, usually denoted by %, is a number or ratio that represents a fraction of 100.
If the problem states that the gym's employees sold 70% (70 percent) more memberships than last year, and it's employees sold 5,190 gym memberships last year, then
memberships this year = 70% more than last year
memberships this year = 70%(5,190) + 5,190
memberships this year = 3,633 + 5,190
memberships this year = 8,823
Hence, the gym's employees sold 8,823 memberships this year.
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y-7=8
What’s the value of y
Answer:
y= 15
Step-by-step explanation:
well I did first was I took eight and added seven because we're trying to find out what why is and whatever why is y - 7 is 8 so I added eight and seven together to get 15 and then I subtracted something and got me beat again .
Use the following bowling scores for six members of a bowling team: 175,210,180,195,208,196 .What is the mean of the scores?
Answer:
1000.6 (The 6 is a repeating so make sure to put a line over it)
Step-by-step explanation:
175+210+180+195+208+196
1164/6
1000.6 ( Put line over 6 is repeating decimal )
Simplify 8x + 9 - 4x - 2.
Answer:
4x + 7
Step-by-step explanation:
8x + 9 - 4x - 2 ← collect like terms
= (8x - 4x) + (9 - 2)
= 4x + 7
x+3y-z=2
x+y-z=0
3x+2y-3z=-1
Answer:
add the like terms if there's no like the answer will be 3x+2y-3z=-1
Find the measures of each numbered angle.
c. ∠ 4
Measure of angle 4 i.e. m∠4 = 50°
What is measurement of an angle ?The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.
In the question,
Let given angle is ∠8.
Given, ∠8 = 50°
Now, according to vertical angle property
∠5 = ∠8
therefore, ∠5 = 50°
Also, ∠5 = ∠4 (alternate interior angles)
Thus, m∠4 = 50°
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The complete question is :
Find measures of numbered angle.
a. ∠2
b. ∠3
c. ∠4
Find the geometric mean between pair of numbers.
40 and 15
The value of the geometric mean of the numbers 40 and 15 is.
Gm ( 40, 15) = 10√6
What is the geometric mean?The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:
Gm (a,b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 40b = 15We substitute and solve for the square root
Gm (40, 15) = √40×15
Gm (40, 15) = √600
Gm (40, 15) = √6×100
Gm ( 40, 15) = 10√6
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Below are two parallel lines with a third line
intersecting them.
46°
What is x equal to?
Answer:
x = 134°
Step-by-step explanation:
The angle labelled [tex]x^{\circ}[/tex] and the 46° add up to 180° as they are co-interior angles.
∴ [tex]x^{\circ} + 46^{\circ} = 180^{\circ}[/tex]
⇒ [tex]x^{\circ} = 180^{\circ} - 46^{\circ}[/tex] [Subtracting 46° from both sides]
⇒ [tex]x = 134^{\circ}[/tex]
Therefore [tex]x[/tex] is equal to 134°.
Find the sum of each finite series. Σ⁹ n=1 (-1)ⁿ . . . . 2
The sum of the given finite series is -1
The given series is:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}[/tex]
The summation notation tell us that we need to add each term (-1)ⁿ as n moves from 1 to 9.
Let us expand this summation notation:
n = 1 ⇒ a(1) = (-1)¹ = -1
n = 2 ⇒ a(2) = (-1)² = 1
n = 3 ⇒ a(3) = (-1)³ = -1
We can continue to expand until n = 9, but we can see the pattern. The series can be written as:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1[/tex]
We can see that a(1) and a(2) are cancelled out to each other. This applies to each pair of consecutive odd and even terms. Each term is cancelled out except a(9). Therefore:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1=-1[/tex]
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The coordinates of the vertices of quadrilateral are A(-6,-1),B(-5,2),C(-1,-5), and D(0,-2). Parker states that quadrilateral is a parallelogram. Prove or disprove Parker’s statement.
=======================================================
Explanation:
Use the slope formula to find the slope of the line through A(-6,-1) and B(-5,2)
[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-5,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - (-1)}{-5 - (-6)}\\\\m = \frac{2 + 1}{-5 + 6}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope of segment AB is 3.
-------------
Repeat these set of steps for segment CD
C = (-1,-5)
D = (0,-2)
[tex](x_1,y_1) = (-1,-5) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-5)}{0 - (-1)}\\\\m = \frac{-2 + 5}{0 + 1}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope of segment CD is also 3
Parallel lines have equal slopes, but different y intercepts.
Since AB and CD have the same slope of 3, this shows AB is parallel to CD.
--------------
Now find the slope of segment BD
B = (-5,2)
D = (0,-2)
[tex](x_1,y_1) = (-5,2) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 2}{0 - (-5)}\\\\m = \frac{-2 - 2}{0 + 5}\\\\m = -\frac{4}{5}\\\\[/tex]
Segment BD has a slope of -4/5
--------------
Lastly, compute the slope of segment AC
A = (-6,-1)
C = (-1,-5)
[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-1,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - (-1)}{-1 - (-6)}\\\\m = \frac{-5 + 1}{-1 + 6}\\\\m = -\frac{4}{5}\\\\[/tex]
Segment AC has a slope of -4/5
Both segments BD and AC have the same slope of -4/5.
Therefore, segments BD and AC are parallel
----------------
We have two pairs of opposite parallel sides. Ultimately figure ABDC is a parallelogram
See the diagram below.
Determine the slope of the line that contains the given points.
T(-6,-11), V(-12,-10)
The slope of the line containing (-6,-11) and (-12,-10) is (-1/6).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -10 , [tex]y_{1}[/tex] = -11 , [tex]x_{2}[/tex] = -12 , and [tex]x_{1}[/tex] = -6 .
On substituting the values of variables in equation1, we will get
m = ( (-10)-(-11) ) / ( (-12)-(-6) ) = (1/(-6)) = (-1/6).
As the slope of a line is (-1/6), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (-6,-11) and (-12,-10) is (-1/6).
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Megan recorded the temperature in her garden each morning for 6 days. The mean of her six recorded temperatures was 2.1 °C. The temperature on one of the days was 4.1 °C. What was the mean of her other 5 recorded temperatures? Give your answer as a decimal.
The mean of the remaining temperature will be 1.7°C
How to calculate the value?Since the mean of her six recorded temperatures was 2.1 °C, the total temperature will be:
= 6 × 2.1
= 12.6°
Since the temperature on one of the days was 4.1 °C, the mean of the remaining temperature will be:
= (12.6 - 4.1)/5
= 8.5 / 5
= 1.7
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Suppose a is a 57 matrix. How many pivot columns must a have if its columns span ? why?.
There must be pivot columns in the matrix. "A has a pivot place in every row" and "A's columns span an R5" seem to be logically equivalent.
What is defined as pivot columns?When a matrix has been in row-echelon form, the first nonzero entry in each row is referred to as a pivot, as well as the columns wherein pivots appear are referred to as pivot columns.
If two matrices in row-echelon form seem to be row-equivalent, their pivots are in the exact same locations.In the question asked, if the column of the 5x7 matrix is equal to R5, and the A span is equal to R5, and the value of A has a pivot for each row, then the position of each pivot in the separate columns of A has the 5 pivot columns.The matrix must contain pivot columns. "A has a pivot position in each row" & "A's columns span an R5" appear rationally equivalent.
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The correct question is-
Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R⁵? Why?
An artist uses gold leaf foil in his work. he wants to cover a piece of canvas that is 22.5 by 34 inches with this foil. the foil costs $4.15 per square inch. how much money will the artist spend on gold leaf foil for his project?
If an artist uses gold leaf foil in his work and he wants to cover a piece of canvas that is 22.5 by 34 inches with this foil and the foil costs $4.15 per square inch, then the money the artist spent on gold leaf foil for this project is equal to $3174.75
The money spent on gold leaf foil for the project can be calculated by the multiplication of the area or square inch of the foil needed to cover the piece of canvas with the price per square inch.
The area or square inches can be calculated by multiplying the length in inches by the width in inches.
Area = 22.5 × 34
Area = 765 square inches
Now, money spent on gold leaf foil can be calculated by multiplication of the area of the need with the price per square inch.
Area × price per square inch
765 × 4.15 = $3174.75
Hence the money the artist spent on gold leaf foil is calculated to be $3174.75
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please help
ASAP HELPP
From the given graph, we have that:
The constant of the relationship on the graph is of 5.The point (7,35) in the proportional relationship graphed in this problem means that 35 gallons of water were used in 7 minutes.What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
In the case of an inverse relationship, we have that:
y = k/x.
k is the constant of proportionality for both cases.
For this problem, the function goes through point (2,10), that is, when x = 2, y = 10, meaning that we can find the constant k as follows:
2k = 10
k = 10/2
k = 5.
The constant of the relationship on the graph is of 5.
For the relationship, we have that:
The input x is the time in minutes.The output y is the water used in gallons.Hence:
The point (7,35) in the proportional relationship graphed in this problem means that 35 gallons of water were used in 7 minutes.
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Question:
Which part of the story begins the development of a character? (5 points)
Exposition
Climax
Falling action
Resolution
Answer: It is (3,5) other one is 5. I did two of them lol.
Position and label each triangle on the coordinate plane. (Lesson 4-8)
Isosceles ΔQRT with base QR that is b units long.
The isosceles triangle's base can be positioned along the x-axis. Because QR is b units long, you can position point R along the x-axis and calculate the coordinates (b, 0).
What is meant by an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
By putting Q at the origin, the isosceles triangle's base can be positioned along the x-axis. Because QR is b units long, you can position point R along the x-axis and calculate the coordinates (b, 0). Because the vertex of the isosceles triangle, point T, is directly above the midpoint of the base, its x-value is half the length of QR and its coordinates are (b/2, c).
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find the volume of the cylinder
Area of base:
3 * 9 = 27
27*9 = 243So, 243 is the answer.
State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
The set of all possible outcomes is the sample space.
True, this sentence is true .
The set of all possible outcomes is the sample space.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.True, this sentence is true .
The set of all possible outcomes is the sample space.
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Fireworks are shot from a barge in a river There is an explosion circle inside which all n the fireworks will explode. Spectators sit outside â safety circle 800 feet from the center of the fireworks display.
a. Find the approximate circumference of the safety circle.
The approximate circumference of the safety circle is 5026.54825 meters.
What do we mean by a circle?A circle is a shape formed by all points in a plane that are at a given distance from the center. It is the curve traced out by a point moving in a plane so that its distance from a given point remains constant. The radius is the distance between any two points on a circle and the center. Typically, the radius must be a positive number. A degenerate case is a circle with r = 0. Except where otherwise noted, this article is about circles in Euclidean geometry, specifically the Euclidean plane.To find the circumference:
Formula: 2πrRadius = 800 metersSo,
C = 2πrC = 2π800C = 5026.54825Therefore, the approximate circumference of the safety circle is 5026.54825 meters.
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how do you do factors of 5 grade
Answer:
If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.
Step-by-step explanation:
Solve: 212x +41 = 32
I need help plssss
Identify what you need to know. Then use the information in the problem to solve.
Which triangles are not necessarily similar?
F. two right triangles with one angle measuring 30°
G. two right triangles with one angle measuring 45°
H. two isosceles triangles
J. two equilateral triangles
Two isosceles triangles are not necessarily similar triangles.
Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.
Analyzing each statements:
F. two right triangles with one angle measuring 30°
- these two triangles have angles measuring 90°, 30°, and 60°
- they both have equal angle measurements
∴ they are similar triangles
G. two right triangles with one angle measuring 45°
- these two triangles have angles measuring 90°, 45°, and 45°
- they both have equal angle measurements
∴ they are similar triangles
H. two isosceles triangles
- isosceles triangles are triangles that have two sides of equal lengths
- two isosceles triangles are similar if the angle of one is congruent to the corresponding angle of the other
∴ they are not necessarily similar, unless stated that their corresponding angles are equal
J. two equilateral triangles
- all equilateral triangles of any side lengths are considered similar triangles as each of its corresponding sides are proportional
∴ they are similar triangles
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