Emanuel used the calculations below to find the product of the given fractions. In which step did his error occur?
Answer:
Emanuel made huis mistake in first step and step 1 is incorrect.
Step-by-step explanation:
The given expression is
[tex](\frac{3}{5})(\frac{4}{9})(-\frac{1}{2})[/tex]
It can be written as
[tex]\frac{3}{5})(\frac{4}{9})(\frac{-1}{2}[/tex]
Step 1: [tex](\frac{(3)(4)(-1)}{(5)(9)(2)})[/tex]
Emanuel used negative sign with both numbers 1 and 2. Therefore the first step of Emanuel is incorrect.
Step 2: [tex]\frac{-12}{90}[/tex]
Step 3: [tex]\frac{-2}{15}[/tex]
Therefore Emanuel made huis mistake in first step and step 1 is incorrect.
Four subtracted from the reciprocal of a number
Which quadrilateral has two pairs of different but equal adjacent sides?
Suppose that water is stored in a cylindrical tank of radius 5 m. if the height of the water in the tank is h, then the volume of the water is v = Ïr 2h = (25m2)Ïh = 25Ïh m2. if we drain the water at a rate of 250 liters per minute, what is the rate at which the water level inside the tank drops?
To calculate the rate at which the water level drops, use the formula dh/dt = dV/dt / (25Ï) and the given drainage rate of 250 liters per minute. The resulting rate is -0.01/Ï meters per minute, which represents the speed of the water level decreasing.
Explanation:To determine the rate at which the water level inside the cylindrical tank drops, we use the given volume formula of the cylinder, V = 25Ï h, where V is volume in cubic meters, h is height in meters, and Ï is the constant pi (approximately 3.14159).
Draining the tank at a rate of 250 liters per minute corresponds to a volume rate of 0.25 cubic meters per minute (since 1 cubic meter equals 1000 liters). Using the formula dV/dt = 25Ï dh/dt, we want to find the rate dh/dt at which the height of the water decreases.
Rearranging for dh/dt gives us dh/dt = dV/dt / (25Ï). Substituting the known rate of volume change, dV/dt = -0.25 m³/min (negative because the volume is decreasing), we get dh/dt = -0.25 / (25Ï), which simplifies to dh/dt = -0.01 / Ï meters per minute. Therefore, the rate at which the water level drops is -0.01/Ï meters per minute.
A rectangle has perimeter 74 cm and length 28. What is its width?
What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56 ?
Answer:the answer would be c which is 146
Step-by-step explanation:
5 more than twice x (algebraic expression)
A football team loses 4 yards on each of three plays. Then they complete a pass for 9 yards. What is the change in yardage after this four plays?
Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x –
What are the solutions of –x2 + 4x = x – 4?
The solutions of the equation [tex]-x^2+4x=x-4[/tex] is:
x= -1 and x=4
Step-by-step explanation:The solution of the graphs of the equation is equal to the x-value of the point of intersection of the graph of two functions i.e. the function on the left side of the equality on the right side of the equality.
Here, the expression is:
[tex]-x^2+4x=x-4[/tex]
Hence, we will see at which point the graph of:
[tex]y=-x^2+4x[/tex]
and [tex]y=x-4[/tex] meet.
The point of intersection of the graph is: (-1,-5) and (4,0).
Hence, the solution of the graph is: x= -1 and x=4
the number of eggs e in the carton and the total costs t of the eggs. what is the dependent variable
The total costs t of the eggs is the dependent variable.
What are independent and dependent variables?Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.
Thus if variable is taking its values independently of any visible direct cause, then that variable is called independent variable.
The variables that take their values based on some other variables' values are called dependent variables.
Given that the number of eggs e in the carton and the total costs t of the eggs.
Here, we know the number of eggs, e, to know how much it costs.
Hence, it is the dependent variable.
Learn more about variable;
https://brainly.com/question/1479694
#SPJ5
a carpenter is measuring a board with which he is working. because one end of the measuring tape is unreadable, the carpenter places the measuring tape so that one end of the board is at 3 inches and the other is at 15 inches. how long is the board?
Answer:
12 inches
Step-by-step explanation:
15 - 3 = 12
The board is 12 inches long.
_____
A measuring tape is like a number line. To find the distance between two numbers on the number line, you subtract the smaller one from the larger one. The tape measure works the same way. Subtract the number at one end of the board from the number at the other end of the board to find the length of the board.
A comuter has $245 in his commuter savings account b. How much must he add to his account if he wants to have 20 weeks worth of tickets in his account
The 6 consecutive integers below add up to 447. x − 2 x − 1 x x + 1 x + 2 x + 3 what is the value of x ? f. 72 g. 73 h. 74 j. 75 k. 76
The value of x is 75.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
6 consecutive integers are x − 2, x − 1, x, x + 1, x + 2, x + 3
Now, the integers add up to 447.
So, x-2 + x-1 + x+ x +1 + x+2 + x+3= 447
6x -3 + 6 = 447
6x = 450
x= 75
Hence, the value of x is 75.
Learn more about algebra here:
https://brainly.com/question/24875240
#SPJ5
The system of inequalities and graph the solution on the graph.
please help me on math???
What is the slope of a line that is parallel to the line shown?
Isaac read a total of 20 books over 5 months. After belonging to the book club for 7 months, how many books will Isaac have read in all? Assume the relationship is directly proportional.
(easy question i just forgot how to do it lol)
20 books / 5 months = 4 books per month
4 books * 7 months = 28 books total
unit 0 algebra review functions graphing linear equations
the population pf a city is 2,500. if the number of males is 240 more than the number of females how many males and females are there in the city
You need to represent the number of males in terms of females.
Explanation:Since you know the number of males relative to females, it makes sense to represent the number of females as a variable, let's say f.
So then the number of males is f+240 and we know that the number of males plus the number of females is 2500. Knowing this, we can write an equation: f+(f+240)=2500. I put the number of males in brackets there just to make it easy to recognize.
This equation can be condensed into 2f+240=2500 and then solved:
2f=2500−240
f=2500−2402
f=1130
Then, we know the number of females, and we can solve for the number of males from here using our male formula: males=f+240. You should then get 1370 as the number of males.
Checking this answer, we see that 1130 + 1370 does equal 2500.
3a+20=-25 what is the value of a?
Triangle QRS is a right triangle.
ΔSTR ~ Δ____
A. ΔTQR
B. ΔRST
C. ΔSQR
D. ΔRTQ
Answer: C. ΔSQR
Step-by-step explanation:
In [tex]\triangle{STR}[/tex] and [tex]\triangle{SQR}[/tex], we have
[tex]\angle{TSR}\cong\angle{OSR}\\\\\angle{STR}\cong\angle{QRS}=90^{\circ}[/tex]
By AA- similarity postulate , we get
[tex]\triangle{STR}\sim\triangle{SQR}[/tex]
AA-similarity postulate says that two triangles are said to be similar if they have two corresponding angles that are congruent or equal in measure.The perimeter, P, of a rectangle is the sum of twice the length and twice the width.
P = 2(l+w) units
P = 2(5)+2(9) units
P = 4x units
P = (l+l)+(w+w) units
P = 2(x+3) units
Answer:
P=2(l+w)
Step-by-step explanation:
It is given that perimeter, P, of a rectangle is the sum of twice the length and twice the width.
Let length of rectangle is l and width of the rectangle is w.
Perimeter = 2 × Length + 2 × Width
[tex]P=2\times l+2\times w[/tex]
[tex]P=2l+2w[/tex]
Taking out common factors.
[tex]P=2(l+w)[/tex]
[Note: (l+l)+(w+w) units is also true but according to the statement only option 1 is true]
Therefore, the correct option is 1.
The membership of a committee consists of 3 english teachers, 4 mathematics teachers, and 2 social studies teachers. if 2 committee members are to be selected at random to write the committee's report, what is the probability that the two members selected will both be english teachers?
The number of students at Valley View Middle School increased by 10%, to 770 total students. How many students were enrolled at Valley View Middle School before the increase?
There are 700 students were enrolled at Valley View Middle School before the increase.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The number of students at Valley View Middle School increased by 10%, to 770 total students.
Now,
Since, The number of students at Valley View Middle School increased by 10%,
And, The number student after the increase = 770
So, We can formulate;
The number of students before the increased is calculated as;
= 770 / (1 + 10%)
= 770 / 1.1
= 700
Thus, There are 700 students were enrolled at Valley View Middle School before the increase.
Learn more about the percentage visit:
https://brainly.com/question/843074
#SPJ2
Solve for a. 3a+1>−7a−14−4
Determine the amount of an investment if 5000 is invested at an interest rate of 4.5% compounded monthly for 10 years. Round your answer to the nearest whole dollar
The amount of an investment of $5,000 at an interest rate of 4.5% compounded monthly for 10 years will be $7,847, rounded to the nearest whole dollar.
Explanation:To determine the amount of an investment that starts at $5,000, with an interest rate of 4.5% compounded monthly for 10 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per unit t.t is the time the money is invested for in years.Plugging the values into the formula:
A = 5000(1 + 0.045/12)^(12*10)
A = 5000(1 + 0.00375)^(120)
A = 5000(1.00375)^(120)
A = 5000 * 1.569463137
A = $7,847 (rounded to the nearest whole dollar)
The amount of the investment after 10 years, compounded monthly at 4.5% interest, will be $7,847.
A piece of string is 325 centimeters long. You need the string to be 1 1/4 meters long. How many centimeters should you cut off
Subtracting 3xy2 from 8xy2 gives the same result as the expression
A.7xy^2-2xy^2
B.-7xy^2-2xy^2
C.3xy^2-8xy^2
8-3 = 5
7-2 = 5
so the answer would be A
The decay of 230 mg of an isotope is described by the function A(t)= 230e-0.031t, where t is time in years. Find the amount left after 26 years. Round your answer to the nearest mg.
Answer:
103 mg.
Step-by-step explanation:
We have been given that the decay of 230 mg of an isotope is described by the function [tex]A(t)=230e^{-0.031t}[/tex], where t is time in years.
To find the amount left after 26 years, we will substitute [tex]t=26[/tex] in our given function as:
[tex]A(26)=230e^{-0.031\cdot 26}[/tex]
[tex]A(26)=230e^{-0.806}[/tex]
Using exponent property [tex]a^{-n}=\frac{1}{a^n}[/tex], we will get:
[tex]A(26)=230\times \frac{1}{e^{0.806}}[/tex]
[tex]A(26)=\frac{230}{e^{0.806}}[/tex]
[tex]A(26)=\frac{230}{2.2389343}[/tex]
[tex]A(26)=102.72744\approx 103[/tex]
Therefore, 103 mg of isotope will be left after 26 years.
How do you factor 8x^2+18x+9=0