a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23
b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1
c. the number of monthly calls x is x > 100
What is inequality ?
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Plan 1: $23 per month for unlimited calls
Plan 2: $19 per month + $0.04 per call
Let the number of calls be x
a. 19 +0.04x >23
0.04x >4
x > 100
b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.
On solving the above inequality, we get over 100 calls should be made so that Plan 1 is more economical than Plan 2.
c. x > 100
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A school is studying Math for Data and Financial Literacy standardized test scores. Which of the following displays could be used to represent the data, and why?
Bar chart, because test scores are numerical
Box plot, because test scores are categorical
Circle graph, because test scores are categorical
Stem-and-leaf-plot, because test scores are numerical
its stem and leaf just took the test
Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.
What is the Stem and leaf plot?In order to help visualize the shape of a distribution, a stem-and-leaf presentation or stem-and-leaf plot is a tool for displaying quantitative data in a graphical manner, comparable to a histogram. They are helpful tools for exploratory data analysis and developed from Arthur Bowley's work in the early 1900s.
This is simply accomplished by creating a draft of the unsorted leaves before arranging them in the final stem-leaf display. On the Undergraduate and graduate levels, you may find a number of examples that have been solved and even obtain expert assistance to learn the subject of stem and leaf plots.
A school is studying Math for Data and Financial Literacy standardized test scores.
Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.
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The section of a window consists of a rectangle surmounted by and equilateral triangle. If the perimeters be given as 10ft, find the dimensions of the window in order that the maximum amount of light may be admitted.
100 POINTS PLEASE
Answer:
Solution
verified
Verified by Toppr
Correct option is C)
Perimeter of window P=2y+3x=16
⇒y=
2
16−3x
....(1)
Area A=xy+
4
3
x
2
=
4
3
x
2
+x(
2
16−3x
)
A=8x+(
4
3
−
2
3
)x
2
dx
dA
=8+(
4
3
−
2
3
)2x
For maxima or minima,
dx
dA
=0
⇒4−
4
(6−
3
)
x=0.
∴x=
6−
(3)
16
=
36−3
16(6+
3
)
=
33
16(6+1.73)
=
33
16(7.73)
=
33
123.68
⇒x=3.75 nearly.
Now,
dx
2
d
2
A
=2(
4
3
−
2
3
)<0
Hence A is maximum.
By (1),
y=2.375
Step-by-step explanation:
The mean of a distribution of test scores is 80. The standard deviation of the scores is 10. If every
score is doubled and 15 is added to each score, what would the new mean and standard deviation be?
The new mean of a distribution of tests would be 175 and the new standard deviation of a distribution of tests would be 10 which is unchanged.
We have been given that in the question:
Mean of data = 80
Standard deviation = 10.
Then, every score is doubled and 15 is added to each score.
What is the mean of a distribution?The mean of a distribution is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
a) Mean of new data
The mean of the data rises by the same amount when a constant value is applied to each observation.
Mean of new score =
μ' = 2μ + 15 = 2(80) + 15 = 175
b) Standard deviation of new data
Every observation has a constant value added to it, therefore the standard deviation stays constant.
The standard deviation of the new score =
σ' = σ = 10
Therefore, the new mean and standard deviation would be 175 and 10 respectively.
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The sale price of a item is $300 after a 25%
Answer:
the answer is 225
Step-by-step explanation:
[tex] \frac{300 \times 25}{100} = 75[/tex]
this is the amount of discount
so remove it from the original price
300 - 75 = 225
which is the price after the 25% discount
hope this helps
Look at this bag of marbles. If you reached into this bag of marble and drew out one marble, find the probability that the marble that you drew was either
blue or green. State your answer as a decimal or a percent.
P (blue or green) there are 4 blue ,3 green , 1 yellow and 2 red
The probability that the marble that you drew was either blue or green is 0.7.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
There are 4 blue ,3 green , 1 yellow and 2 red
In total there are 10 balls.
probability of getting blue or green ball is = 7/10
P (blue or green) = 0.7
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Simplify
(Show work)
−6(x−2)+5
Answer:
-6x+17Step-by-step explanation:
[tex]−6(x−2)+50\\\\-6x+12+5\\\\\sf{-6x+17}[/tex]
we are done!! ~~
Answer:
-6x + 17
Step-by-step explanation:
We can use algebraic expansion and order of operations to solve for this expression.
[tex] - 6(x - 2) + 5 \\ = - 6x + 12 + 5 \\ = - 6x + 17[/tex]
(3g) ^ 4 i need an expression of what it’s equal to
Answer:
[tex] 81g^4 [/tex]
Step-by-step explanation:
When you raise a product to a power, raise each factor of the product to the power.
Rule:
[tex] (ab)^n = a^nb^n [/tex]
Our problem:
[tex] (3g)^4 = 3^4g^4 = 81g^4 [/tex]
what is 36 divided by 7.2
Answer:
36÷7.2=5
So this is the answer
Squere root
Find the using division methos
15384
The square root of the 15384 by division method is a 124.032.
According to the statement
We have to find that the square root with the division method.
So, For this purpose, we know that the
The long division is the mathematical method for dividing large numbers into smaller groups or parts
And
A generalised version of this method called polynomial long division is also used for dividing polynomials
From the given information:
The number is a 15384.
And then
Firstly in this number by the squaring of the same number and by this method after going down until the remainder is zero.
And after solving the square root of 15384
The answer will become 124.032.
So, The square root of the 15384 by division method is a 124.032.
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9xy-22
Term(s):
Coefficient(s):
Variable(s):
Constant(s):
Answer:
Coefficient(s):9
Variable(s):x,y
Constant(s):-22
Step-by-step explanation:
Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. If a and b are negative, then a + b is also negative.\
Answer:
The conditional statement is true.
Step-by-step explanation:
If a and b are negative, it doesn't matter what numbers they are; the sum will always be negative.
CA=√(d-e²)=d-e
7. (√1+d²)² + (√²+1)'. =?
(1 + ²) + (e²+1)
8.
9.-1 MABMBC
=
2
2+d²+e² =
2 =
-1 = de
OA. -2de
OB. (A + B)2
OC. A²+ B²
OD. (d-e)2
d²2de + e²
d²2de + e²
-2de
Which expression is missing from step 7?
Pythagorean theorem
simplify
substitution property of equality
Answer: [tex]A^{2} + B^{2}[/tex] correct answer.
Step-by-step explanation:
What is Pythagorean Theorem?
Image result for Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation.
[tex]A^{2} + B^{2} + C^{2}[/tex]
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
So, We can write,
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
[tex]Hypotenuse^{2}[/tex] = [tex]Perpendicular^{2}[/tex] + [tex]Base^{2}[/tex]
[tex]C^{2} = A^{2} + B^{2}[/tex]
Hence,
[tex]A^{2} + B^{2}[/tex] correct answer.
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Determine whether each sequence is geometric. If so, find the common ratio. -1,1,-1,1, . . . . .
The given sequence is geometric, with common ratio = -1.
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.Now, Given: -1, 1, -1, 1, ...
Here, a₁ = -1, r = [tex]\frac{1}{-1}=\frac{-1}{1} = \frac{1}{-1} = -1[/tex]
Hence, it is a geometric sequence, with common ratio = -1.
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Give the domain and range of the quadratic function whose graph is described.
The vertex is (-5, -8) and the parabola opens up.
The domain of f is ?
The domain of f is [-5, ∞) because the vertex is the global minimum of a parabola that opens up.
The domain of any polynomial, including quadratics, is (–∞, ∞).
The domain of a parabola is always all real numbers (sometimes written (−∞,∞). The domain is all real numbers because every single number on the x− axis results in a valid output for the function (a quadratic).
When x=−b2a, y=c−b24a. Therefore the maximum or minimum value of the quadratic is c−b24a. Whether it is the maximum or minimum can be determined by examining the sign of a. If a is positive, then the range is y≥c−b24a
Hence, The range here is [-5, ∞), because the vertex is the global minimum of a parabola that opens up, and the global minimum is the lowest value.
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Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple formula or rule.
Answer:
3 5,7,9,11,13,16,17 19,21,23,25,27,29
Use the graphs of f and g to graph h(x)=(f+g)(x). I need help with #4.
Answer:
My teacher helped
Step-by-step explanation:
Find the distance between each pair of parallel lines with the given equations.
y=4 x
y=4 x-17
The distance between the given parallel lines is
In the given statement is :
The equations of the pair of each parallel lines is:
y = 4x and y = 4x - 17
To find the distance between each pair of parallel lines.
Two lines a₁x +b₁y + c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
As we know that distance between the parallel lines (d) is given as:-
d = [tex]\frac{c_{2} -c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]
Parallel lines equation as:
y - 4x = 0
y - 4x + 17 = 0
Here,
a = -4 , b = 1, c1 = 0, c2 = 17
Therefore, putting the values
d = [tex]\frac{17 -0}{\sqrt{-4^{2}+1^{2} } }[/tex]
d = [tex]\frac{17}{\sqrt{17} }[/tex]
d = root 17
d = 4.12 units
Hence, The distance between the given parallel lines is 4.12 units
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two non-zero real numbers, a and b, satisfy ab=a-b. Find a possible value of [tex]a/b +b/a -ab[/tex]
100 points
Answer:
2
Step-by-step explanation:
Given equations:
[tex]\begin{cases}ab=a-b\\\\\dfrac{a}{b}+\dfrac{b}{a}-ab\end{cases}[/tex]
Rewrite the second equation as a rational expression:
[tex]\begin{aligned}\implies \dfrac{a}{b}+\dfrac{b}{a}-ab & = \dfrac{a}{b} \cdot \dfrac{a}{a}+\dfrac{b}{a} \cdot \dfrac{b}{b}-ab\cdot \dfrac{ab}{ab} \\\\&=\dfrac{a^2}{ab}+\dfrac{b^2}{ab}-\dfrac{(ab)^2}{ab}\\\\&=\dfrac{a^2+b^2-(ab)^2}{ab}\\\\\end{aligned}[/tex]
Substitute the first equation [tex]ab=a-b[/tex] into the rational expression:
[tex]\begin{aligned}\implies \dfrac{a^2+b^2-(a-b)^2}{ab}&=\dfrac{a^2+b^2-(a^2-2ab+b^2)}{ab}\\\\&=\dfrac{a^2+b^2-a^2+2ab-b^2}{ab}\\\\&=\dfrac{2ab}{ab}\\\\&=2\end{aligned}[/tex]
Therefore, the possible value of the given expression is 2.
A scientist measures 4.62 ml of a chemical into a beaker. \with a pipette, he carefully takes out 0.67 of the chemical. finally, he adds 1.25 ml of water into the beaker. how much liquid is in the beaker now?
Using basic mathematical operations such as addition and subtraction, the beaker now has 5.2 ml of liquid.
Basic mathematical operations include addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If a scientist measures 4.62 ml of a chemical into a beaker, then takes out 0.67 ml of the chemical, and finally adds 1.25 ml of water into the beaker, subtracting the amount of chemical taken out from the initial amount of chemical and adding the amount of water, we can solve how much liquid is in the beaker.
4.62 ml - 0.67 ml + 1.25 ml = 5.2 ml
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An equilateral triangle has
sides of 4x + 10. Write an
expression for the perimeter of
the triangle.
Determine the value of x when the perimeter is 42.
Answer:
x = 1 if the perimeter is 42
Step-by-step explanation:
Given
s = 4x + 10
when Perimeter = 42, what is x?
Solution
Perimeter = 3s
Perimeter = 3(4x +10) Remove the brackets
Perimeter = 12x + 30
Let the Perimeter = 42
42 = 12x + 30 Subtract 30 from both sides
42-30 = 12x + 30-30 Combine
12 = 12x Divide by 12
12/12 = 12x/12
x = 1
Which of the following numbers is between -3/4 and 5/8
-1
-1/2
7/8
0.9
Answer:
7/8 if you divide you will get your answer
Question 1 of 5
Drag each equation to the correct location on the table.
Solve the equations for the given variable. Then place the equations in the table under the correct solution.
=9
4 = 1
-6+z=-9
x=3
X 3
25= -2 -² + z = ²
Submit
-14z = -42
Reset
The correct location on the table is:
For x=3: x-5= -2, -3/5+x= 12/5, -14x=-42For x≠3: x/3=9, -6+x= -9, x/4= 6/5Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex] .
b= the constant term that represents the y-intercept.
For the given example: a=7 and b=2.
For solving linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.
x/3=9, thusx= 9*3
x=27
Therefore, x≠3
-6+x=-9, thusx=-9+6
x= -3
Therefore, x≠3
x-5=-2, thusx= 5 -2
x= 3
Therefore, x=3
-3/5+x= 12/5, thusx= 12/5 + 3/5
x= 15/5
x=3
Therefore, x=3
-14x=-42, thus14x=42
x=3
Therefore, x=3
x/4= 6/5, thus5x=24x=24/5 Therefore, x≠3Read more about the linear equations here:
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Divide. State any restrictions on the variables.
3 y-12 / 2y+4 ÷ 6y-24 / 8+4 y
The restrictions on the variables x and y of the equation
(3y-12)/(2y+4) ÷ (6y-24)/(8+4y) be y ≠ 4 and y ≠ -2
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)
Let the equation be (3y-12)/(2y+4) ÷ (6y-24)/(8+4y)
simplifying the equation, we get
(3y-12)/(2y+4) × (8+4y)/(6y-24)
⇒ (3y-12)/(2y+4) × 2(4+2y)/2(3y-12)
⇒ 2/2 = 1
What are the restrictions on the variables?If y = 4 ⇒ denominator (6 × 4 - 24) = 0 = ∞
Similarly, If y = -2 ⇒ denominator ((2 × -2) + 4) =0 = ∞
So, y ≠ 4, y ≠ -2
How to find restrictions on the variables?
The denominator determines the restrictions of a rational expression's domain.Find those limitations without regard to the numerator.Set the denominator to 0 and solve the provided expression to discover the domain restrictions.To learn more about restrictions on the variables, refer:
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8th grade mathematics| 50 POINTS
The equation y + 6 = 1/3 (x - 9) is written in point-slope form. What is the equation written in slope-intercept form?
A. y = 1/3 x -3
B. y = 1/3 x + 9
C. y = 1/3 x - 9
D. y = 1/3 x + 3
I appreciate all of your answers, even if they are wrong, if answers are taken up but you still would like to answer, please put in the comments. Have an awesome day!!! :)
C. y = 1/3 x - 9
Step-by-step explanation:The slope-intercept form is one way to represent a linear function that is set equal to y.
Simplifying and Solving
To find slope-intercept form from point-slope you should simplify the equation and then solve for y.
y + 6 = 1/3 (x - 9)Firstly, distribute the 1/3.
[tex]y+6=\frac{1}{3}x-3[/tex]Then, subtract the 6 from both sides.
[tex]y = \frac{1}{3} x - 9[/tex]This means that the slope-intercept form is y = 1/3 x - 9.
What Slope-Intercept Form Shows
We use slope-intercept form for 2 main reasons; it shows the slope and the y-intercept of a line (hence the name). The formula of slope-intercept is y = mx + b. In this formula, m is the slope and b is the y-intercept.
So, the slope of the line above is 1/3. The y-intercept of the line is -9.
from
3. Error Analysis A student claims the
sequence 0,1,3, 6, ... is an arithmetic
sequence, and the next number is 10. What
error did the student make?
The given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
What is an arithmetic sequence?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
here the given sequence is 0,1,3,6,10,......is an arithmetic sequence
then the common difference between the consecutive terms is constant
lets check take two consecutive terms as 0 and 1 then the difference is 1
take 1 and 3 then common difference is 3-1 =2
take 3 and 6 then common difference is 6-3 =3
take 6 and 10 then common difference is 10-6=4
.............in the same way we check for other terms also
and found that the common difference is not same
Hence the given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
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891.8 ÷ 5.2 = pls with the work out to
The answer to your question would be, 171.5
Sketch the region bounded by the curves x=y3,x=1, and y=0 then find the volume of the solid generated by revolving this region about the y-axis.
According to the question, the region is bounded by the curve with the given data as [tex]x = y^{3} , x=1, y=0.[/tex]
To compute the volume of the solid, use the disk method. The given object is rotated along the horizontal axis with the disk cross sectional area and the volume can be written as:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx[/tex]
As per question, when x = 1 then the value of y is: y = 1
Now, substituting calculated values in the expression:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx[/tex]
Substitute the value of the variable 'x':
Therefore, the expression can be written as:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx=\int\limits^0_1 {\pi (y^{3}) ^{2} } \, dx=\frac{\pi }{7}=0.448[/tex]
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Find the slope of the line passing through the points (-5, 2) and (3, -9).
Answer: -8/11
Step-by-step explanation:
apply the formula
x sub 2- x sub 1
over
y sub 2 - y sub 1
yw
solve the equation for the indicated variable
A = 1/2(pi)(r)^2 solve for pi
Answer:
(2A)/(r^2)=pi
Step-by-step explanation:
The goal is to get pi by itself, so you have to move all the other elements over
2A=pir^2
(2A)/(r^2)=pi
Which graph shows a set of ordered pairs that represent a function?
3
2
1 .
5-4-3-2-11. 2.3
-2-
3+
Mark this and return
3-2.
3-
2-
4
+2+
-3-
O
123
5
34
2+
1+
4-3-2-1₁- 1 2 3 4 5
.
Save and Exit
+24
-3-
4
O
4
3-
2
44
54-3-2-11-
•
1 2 3 4 5 X
Next
Submit
The second graph shows a set of ordered pairs that represent a function.
What is function?Functions are an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
here, we have,
A relation is a function in which every x value will have different y values, this represents "every input will have unique output" part of the definition of the function,
When we observe the graphs (attached), we will notice in graph 1) there are two ordered pairs with same x value and different y values, (2, -1) and (2, -3), which is making them out of the list of being a function,
In graph 2) we have, (-2, 2), (1, 1), (5, 4), (-4, -4), (2, -5) and (4, -3), in this all the order pairs have different x-y values, therefore, this set of ordered pairs that represent a function.
Hence, the second graph shows a set of ordered pairs that represent a function.
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The question do not have graph, so, the question is solved for the graph attached.
