The equation we will use is Equation 1: 2x − 3y = 11. The values of x and y are 1 and -3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
Equation 1: 2x − 3y = 11
Equation 2: x + 2y = −5
Now,
Equation 2: x + 2y = −5
x=-5-2y
Substituting the value of x in equation 1
2(-5-2y)-3y=11
-10-4y-3y=11
-10-7y=11
-7y=11+10
-7y=21
y=-3
Substituting the value of y in equation 2
x+2*-3=-5
x=-5+6
x=1
Therefore, the solution of the system of equations will be x=1,y=-3
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A culture of bacteria has an initial population of 920 bacteria and doubles every 7
hours. Using the formula P = Po 22, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 8 hours, to the nearest whole number?
After 13 hours, there are 17,582 people living there, to the nearest whole number.
what is interest rate ?Divide the amount by the cost of capital, the length of time, and other factors to arrive at simple interest. Simple gain = initial + return + hours is the marketing formula. This system makes it easiest to calculating interest. The most conventional technique to figure out interest is as a portion of the principal sum. He will indeed pay his share of the 100percent annual interest, for example, if he borrows $100 from a partner and commits to pay it back with 5% concern. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an extra component of the loan total. The interest on the loan is this percentage.
given
initially populous,
Increased Rate, r = 2
Time-doubling, d=5 Hours
Population after t hours is P(t).
After 13 hours, we want to know how many bacteria are present.
e.g., at t=13 hours
After 13 hours, there are 17,582 people living there, to the nearest whole number.
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How do you simplify 6 1/2 div 2 1/3?
After simplifing [tex]6\frac{1}{2} \ and \ 2\frac{1}{3}[/tex] after dividing the value is [tex]2\frac{11}{14}[/tex]
What are Fractions ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
The numerator of an improper fraction is bigger than the denominator. For instance, 2/3 is a valid fraction since its denominator is bigger than its numerator, but 3/2 is an improper fraction.
The mixed fractions are
[tex]6\frac{1}{2} \ and \ 2\frac{1}{3}[/tex]
The improper fractions are :
13/2 and 7/3
Dividing 13/2 by 7/3 we get the value :
(13/2)/(7/3) = 13/2 * 3/7 = 39/14 = [tex]2\frac{11}{14}[/tex]
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seven people are in an elevator which stops at ten floors.now consider the situation when no two people get off at the same floor. before the elevator begins to travel, each of them pushes a button for his or her floor. in how many ways can the elevator buttons be lighted?
This is simple question , answer is 4 ways
If you double 7 you get
Answer:
49
Step-by-step explanation:
7x7 = 49
you can just square 7 in your calculator
Mrs. Hilt owns a house on a lot shaped like a rectangle. The perimeter
of the lot is 60 feet. What is the length and the width of the lot?
A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot.
A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 4 has one dot, the value of 4.5 has two dots, the value of 5 has two dots, the value of 6 has one dot, the value of 6.5 has two dots, the value of 7 has one dot, and the value of 8 has one dot. The image is titled Ballet Shoe Sizes.
What is the range, and what does it mean in terms of this data set?
The range is 4.5, and it means that the data varies by a value of 4.5.
The range is 3.5, and it means that it is the value that occurs the most.
The range is 4.0, and it means that the data varies by a value of 4.0.
The range is 4.0, and it means that it is the value that is the smallest.
The range is 4.5, and it means that the data varies by a value of 4.5.
What is the data set?A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it.
The range is the difference between the largest and smallest values in a data set.
In this case, the largest value is 8 and the smallest value is 3.5,
so the range is 8 - 3.5 = 4.5.
This means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
Hence, The range is 4.5, and it means that the data varies by a value of 4.5.
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The region bounded by y=6-x^2 and y=2 is revolved about the x-axis. What is the volume of the solid obtained?
The region bounded by y=6-x^2 and y=2 is revolved about the x-axis has the volume as 384pi/5.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have examined the numerous three-dimensional solids and shapes, such as cubes, cuboids, cylinders, cones, etc., in three-dimensional geometry.
The intersection points of y = 6−x^2 and y = 2 are given by the equation 6 − x^2 = 2, i.e., x^2 = 4, so x = −2 and x = 2.
The integration can be written as:
[tex]\int\limits^2_{-2} {\ \pi (y_t^2 - y_b^2) } \, dx \\\\\int\limits^2_{-2} {\ \pi((6 - x^2)^2 - 4)} \, dx \\\\\int\limits^2_{-2} {\ \pi (x^4 - 12x^2 + 32)^2} \, dx\\ \\= \pi [\frac{x^5}{5} - 4x^3 + 32x ]_{-2}^2\\\\= \frac{384 \pi}{5}[/tex]
Hence, the region bounded by y=6-x^2 and y=2 is revolved about the x-axis has the volume as 384pi/5.
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Multiply (2x^2+6x-10)(x^2-2x+2).
complete the first step in dividing the fraction 45 by the fraction 63.45÷63 =
Completed the first step in dividing the fraction 45 ÷ 63 = 45/63 = 7/10.
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Divide 45 by 63 to get the first digit of the quotient:
45 ÷ 63 = 7/10
Multiply 63 by 7/10 to get 45:
7/10 × 63 = 45
Subtract this result from 45:
45 - 45 = 0
Bring down the next digit (i.e., 43) to the next decimal place:
7/10
Repeat the above steps to find the next digit in the decimal expansion of the quotient.
Completed the first step in dividing the fraction 45 ÷ 63 = 45/63 = 7/10.
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Connor is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Connor have to pay for parking if he left his car in the lot for 2 hours? How much would Connor have to pay if he left his car in the lot for
t
t hours?
The equation is given as y = 2t + 9 and Connor would pay $13 if he left his car for 2 hours
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the total money paid for parking for t hours.
There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour. Hence:
y = 2t + 9
To park for 2 hours, t = 2:
y = 2(2) + 9 = $13
The equation is given as y = 2t + 9
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the marks on a statistics midterm are normally distributed with a mean of 78 and a standard deviation of 6. what proportion of the class has a midterm grade of less than 75?
The proportion of the class with a midterm grade less than 75 is approximately 0.3085, or 30.85%. This means that 30.85% of the class is expected to have a midterm grade lower than 75.
We can use the cumulative distribution function (CDF) of the normal distribution to find the proportion of the class with a midterm grade less than 75.
The CDF of a normal distribution with mean μ and standard deviation σ evaluated at a point x is given by the formula:
CDF(x) = 0.5 * [1 + erf((x - μ) / (σ * √2))]
where erf is the error function.
For this problem, μ = 78 and σ = 6, and x = 75, so the CDF can be calculated as follows:
CDF(75) = 0.5 * [1 + erf((75 - 78) / (6 * √2))]
= 0.5 * [1 + erf(-0.3536)]
The value of erf(-0.3536) can be looked up in a table or calculated using a software package. The result is approximately -0.383.
CDF(75) = 0.5 * [1 + -0.383] = 0.5 * [0.617] = 0.3085
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The scientist in the laboratory company raise amoebas to sell to schools for use in biology classes. They know that one amoeba divides into two amoebas every hour and that formula T equals log two base N can be used to determine how long in hours, t, it takes to produce a certain number of amoebas, N. Determine to the nearest tenth of an hour, how long it takes to produce 10,000 amoebas if they start with one amoeba
it takes approximately 14 hours to produce 10,000 amoebas, rounded to the nearest tenth of an hour.
The formula T = [tex]log^2[/tex] N can be used to determine the number of hours, T, it takes to produce a certain number of amoebas, N.
We can use this formula to find the number of hours it takes to produce 10,000 amoebas, given that the scientist starts with one amoeba:
T = [tex]log^2[/tex] N = l[tex]log^2[/tex] 10,000 = 14.000
So it takes approximately 14 hours to produce 10,000 amoebas, rounded to the nearest tenth of an hour.
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Find the coordinates of p so that p partitions segment ab in the part-to-whole ratio of 1 to 5 with a(-9, 3) and b(1, 8). Show your work for full credit. No work - no credit.
The following formula can be used to get the coordinates of P such that P divides segment AB into parts having a part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). P = (1 - t)A + TB.
What is partitions segment?A line segment can be partitioned by splitting it up into the specified number of parts. To determine how many partitions there are in the line segment, add the two values in the ratio. In order for all database nodes to participate in query execution, segmentation seeks to divide data across them uniformly. The CREATE PROJECTION statement's hash segmentation clause allows you to specify segmentation. For distributed computing, partitioning describes the arrangement of data in each node.where A and B are the coordinates of the segment's two endpoints, P's position on the segment AB is represented by the scalar value t, and
The part-to-whole ratio in this situation is 1:5, thus t equals 1/6.
In order to change the values of A, B, and t in the formula, we do as follows:
P = (1 - 1/6)A + (1/6)B
P = (5/6)A + (1/6)B
P = (-95/6, 35/6) + (1/6, 8/6)
P = (-15/2, 5/2) + (1/6, 4/3)
P = (-15/2 + 1/6, 5/2 + 4/3)
P = (-30/3, 23/6)
The positioning of P is (-10,3.83)
Regarding the second issue,
Using the same procedure as before, we can determine P's coordinates such that P divides segment AB in three equal halves if A(7, -4) and
B(-5, 4).
P = (1 - t)A + TB
The part-to-whole ratio in this situation is 3:1, therefore t equals 3/4.
In order to change the values of A, B, and t in the formula, we do as follows:
P = (1 - 3/4)A + (3/4)B
P = (1/4)A + (3/4)B
P = (7/4, -4/4) + (-53/4, 43/4)
P = (7/4 + -15/4, -4/4 + 3)
P = (-8/4, -1/4)
The positioning of P is (-2,-0.25)
Point P in the first issue is hence (-10,3.83), while Point P in the second issue is (-2,-0.25)
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How do i do this and answer pls
marshall would like to get an idea of his monthly electricity expenses. so, he compiles a list of the last several months' electricity bill amounts (rounded to the nearest dollar). these values are given below. use the calculator to draw a histogram for these values using 5 classes. 153,141,108,198,190,107,185,165,137,107 marshall finds that if he spent at least $145 in a given month on electricity, he could have saved $10 in that month by conserving in certain ways. based on the histogram produced, how much money could marshall have saved if he would have conserved in those ways?
The money could Marshall have saved if he would have conserved in those ways [tex]T=298N+10[/tex]
Marshall would like to get an idea of his monthly electricity expenses.
So, he compiles a list of the last several months' electricity bill amounts
Marshall finds that if he spent at least $145 in a given month on electricity,
Have saved $10 in that month
We are given the following:
A = 145N + 10
B = 153N
We are required to determine the total amount (P) saved using both plans combined.
This can be achieved thus:
[tex]T=A+B[/tex]
[tex]T = 145N+10+153N[/tex]
[tex]T =298N+10[/tex]
Therefore,
The money could Marshall have saved if he would have conserved in those ways [tex]T=298N+10[/tex]
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help please............
The required quotient of the given expression -2 1/2 / [3/4] is given as -2.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= -2 1 / 2 [3/4]
= -3/2 × 4 / 3
= -2
Thus, the required quotient of the given expression -2 1/2 / [3/4] is given as -2.
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solve x^2-12x+18=0 by completing the square
The answer to the equation is x = 6 or x = 6.
How the answer was obtainedTo solve the equation x^2 - 12x + 18 = 0 by completing the square, follow these steps:
Rewrite the equation in the form (x - a)^2 = b, where a and b are constants. In this case, a = 6 and b = 0.
Add (a^2 - b) to both sides of the equation to complete the square.
x^2 - 12x + 36 = 18
Factor the left side of the equation as a perfect square trinomial.
(x - 6)^2 = 0
Take the square root of both sides of the equation.
x - 6 = 0 or x - 6 = 0
Solve for x by adding or subtracting a to both sides of the equation.
x = 6 or x = 6.
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3.) A caterer charges $120 to cater a party for 15 people and $200 for 25 people. A.) Write an equation using x and y to find the cost of having a party catered depending on the number of people attending. B.) Describe what the x and y variables represent in your equation. C.) Use your equation to predict how much it will cost to have a party of 40 people catered. Show your work.
Answer: A) The equation can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope represents the cost per person and the y-intercept represents the fixed cost. Using the two given points, we can find the slope and y-intercept:
(15, 120) and (25, 200)
m = (200 - 120) / (25 - 15) = 80 / 10 = 8
b = 120 - 8 * 15 = 120 - 120 = 0
So the equation is y = 8x.
B) In the equation y = 8x, x represents the number of people attending the party and y represents the cost of having the party catered.
C) To predict the cost of having a party of 40 people catered, we plug in x = 40 into the equation:
y = 8x
y = 8 * 40
y = 320
So it will cost $320 to have a party of 40 people catered.
Step-by-step explanation:
215.7 is what percent of 192
112.34375%
215.7 is 112.34400% of 192
you want to draw an enlargement of a design that is printed
The dimensions of the largest complete enlargement are
[tex]8\frac{1}{2} and10\frac{5}{8} inches[/tex].
A scale factor is defined as a number by which the size of any geometrical figure or shape can be changed with respect to its original size.
we know that
If two figures are similar, then the scale factor is the ratio of their corresponding sides
first, we have to divide 8 1/2 by 4
8 1/2=8*2+1/4=17/2
so
17/2=2.125 inches.
Now divide 11 by 5.
11/5=2.2.
The final step is to find the largest complete enlargement and the scale factor is the smaller of the two previous values
The scale factor=2.125
The dimensions are
4*2.125=8.5=8 1/2
5*2.125=10.625=10 5/8
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I need an answer to my math test i cant answer the question.
It is a proportionate relationship if the ratio remains not constant constant.
What kind of relationship is proportional?As an illustration of a proportionate relationship in real life, let's look at the following: There is a correlation between the number of gallons of gas we put in our car and the price we will have to pay when we fill up the tank. That is to say, the more gas we use, the more we will have to pay.
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. The "constant of proportionality" is a term used to describe this constant.
Examining the ratios between the two variables will help you determine whether a relationship is proportional. It is a proportionate relationship if the ratio remains constant.
11 $24
36 $39
66 $79
85 $98
It is a proportionate relationship if the ratio remains not constant constant.
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true or false? {8} element of {6, 8, 10, {6}, {8}, {10}}
The elements 7 and 8 are not in the set B. So every element of A is not an element of B. So the Statement is false.
The elements of set A and set B are:
A = {5, 6, 7, 8, 9, 10}
B = {5, 6, 9, 10}
Total elements in set A is 6 and set B is 4.
We have to check every element of A is also an element of B. To check we have see that every elements of set A is in the set B.
The elements of set A 5, 6, 9, 10 are in the set B but the elements 7 and 8 are not in the set B.
So the given statement is False.
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The complete question is:
Determine if the following statement is true or false regarding sets A and B.
A = {5, 6, 7, 8, 9, 10}
B = {5, 6, 9, 10}
Every element of A is also an element of B. Choose the correct answer below.
1. False
2. True
6.4 divided by 49.92
Answer:
1.4024390244 I hope that helps
here is a rectangular prism.
work out the volume and round to 3 significant figures.
7.2cm,8.4cm,18cm
The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.
What is volume?
In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
a rectangular prism with 7.2cm,8.4cm,18cm
we know,
the volume is
V= l.b.w
here,
l= 7.2 cm
b= 8.4 cm
w= 18cm
i.e. V= 1088.64 cm^2
Hence, The volume is 1088.64 cm^2 of a rectangular prism with 7.2cm,8.4cm,18cm.
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Fill in the table using this function rule.
y = 3x+2
X
1
2
7
8
X
y
0
0
0
0
15
The table using this function rule y = 3x+2 is as follows:
x y
1 5
2 8
7 23
8 26
What is function rule?
The relationship between the input or domain and the output or range is represented by the function rule. A relation is a function if and only if each domain value has one value in the range.
An output is produced by a function machine using an input and a set of rules. Connecting a function described by a verbal rule with corresponding values in a table is the goal of this task (one of six connections to be made between the four ways to represent a function, the other two being through its graph and through an expression).
Although this broad application is not meant to be evaluated, it encourages students to think more broadly about functions as relating objects other than numbers.
Given that, y = 3x+2
Below is the completed table,
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A computer originally priced at $990, is reduced by 30%
Answer:
The answer is $297
Answer: The price of the PC is now $693.
Step-by-step explanation:
1. Find 30% of $990.
30% of $990 = $297
2. subtract.
$990 - $297 = $693
Consider functions f and g.
f(x)
g(x)
Which expression is equal to f(x) + g(x)?
=
=
-3x² + 4x + 4
x (-7x - 7)
O A. -10x² 3x + 4
OB.
-3x²
3x
3
O C. -10x² + 4x - 3
4x² 3x + 4
O D.
-
-
-
-
A. -10x^2 - 3x +4 , is the expression is equal to f(x) + g(x).
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
f(x)= -3x^2+4x+4
g(x)= x(-7x-7)
now,
f(x) + g(x)
=-3x^2+4x+4 +x(-7x-7)
= -10x^2 - 3x +4
Hence, A. -10x^2 - 3x +4 , is the expression is equal to f(x) + g(x).
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Identify which of the twelve basic functions fit the description given.
The six functions that are increasing on their entire domains
The six functions that are incresing on their domain are : identity, cubing, square root, exponential, natural log and logistic function.
What is Function ?Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.
The logistic function is a function that simulates the exponential expansion of a population while also taking into account variables like the carrying capacity of land and other considerations.
The inverse of an exponential function, the natural log is the logarithm to the base of the integer e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues. The basis of logarithms and natural logs are exponential functions and logarithmic functions.
The six functions that are incresing on their domain are :
identity, cubing, square root, exponential, natural log and logistic.
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What is the slope of the function y = -2x-3y=−2x−3?
Answer:
The slope of the function y = -2x - 3 is -2. This is calculated by taking the coefficient of the x-term and making it the numerator of a fraction, and making the constant term the denominator.
Step-by-step explanation:
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the symbol for _____ is rhoxy.
Rhoxy is the chemical symbol for Rhodium (Rh).
Rhodium is a transition metal found in group 9 of the periodic table, and its atomic number is 45. Its atomic mass is 102.90550 g/mol. Its atomic radius is 1.36 angstroms and its oxidation state is +3.
Rhoxy can be calculated by taking the atomic mass of Rhodium and converting it to moles. This is done by dividing the atomic mass of Rhodium by the molar mass constant, which is 1.00794 g/mol. This results in 0.1022 moles of Rhodium. The formula for moles of a substance is n = m/M, where n is the moles, m is the mass of the substance, and M is the molar mass constant.
To calculate the amount of Rhoxy, divide the moles of Rhodium by Avogadro’s number (6.02 x 10^23). This results in 1.68 x 10^-24 moles of Rhoxy. The formula for this calculation is n = n/N, where n is the moles of the substance, and N is Avogadro’s number.
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Complete question :
What is the symbol for Rhodium?