Final answer:
To find the number n in the inequality '8 less than a number n is less than 11', we can set up and solve the inequality n - 8 < 11. The answer is that the number n is less than 19.
Explanation:
The question states that 8 less than a number n is less than 11. To solve this, we can set up the inequality:
n - 8 < 11
To isolate n, we can add 8 to both sides:
n < 11 + 8
n < 19
So, the answer is that the number n is less than 19.
The number of private investigators is expected to increase from 52,000 in 2006 to 61,000 in 2016. If there are 648,982 police officers in 2006, how many police officers must there be in 2016 to have a greater percent increase than that of private investigators?
To have a greater percent increase than private investigators between 2006 to 2016, there must be approximately 760,945 police officers in 2016. This is found by applying the formula for percentage increase and adjusting it to find the required final number.
Explanation:The percent increase of private investigators from 2006 to 2016 is found by subtracting the initial number from the final number, then dividing by the initial number and multiplying by 100%. This formula gives us (61000 - 52000) / 52000 * 100 = 17.3%, rounded to the nearest tenth of a percent.
To have a greater increase in police officers than that of private investigators, the percent increase must be more than 17.3%. To find the required number of police officers in 2016, we first express 17.3% as a decimal, which is 0.173. Then we use the formula for percentage increase, which is (final number - initial number) / initial number = percentage increase. By rearranging the formula, we get the required final number = (initial number * percentage increase) + initial number. Substituting the given figures, we have (648982 * 0.173) + 648982 = 760945, rounded to the nearest whole number.
Therefore, there must be approximately 760,945 police officers in 2016 to have a greater percent increase than that of the private investigators.
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8) g(n) = 3n + 2
Perform the indicated operation
f (n) = 2n
2
+ 5
Find g( f (2))
Write your own word problem, then create the slope intercept form equation.
The slope-intercept form equation for the word problem is [tex]\( y = \frac{3}{4}x + 1 \).[/tex]
Let's consider a word problem where a local gym charges a $1 sign-up fee and $3 for every hour of use. If we let [tex]\( x \)[/tex] represent the number of hours a member uses the gym and [tex]\( y \)[/tex] represent the total cost, we can write an equation in slope-intercept form.
The slope-intercept form of a linear equation is given by [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line and [tex]\( b \)[/tex] is the y-intercept.
In this scenario, the slope [tex]\( m \)[/tex] is the cost per hour, which is $3. The y-intercept [tex]\( b \)[/tex] is the initial sign-up fee, which is $1.
Therefore, the equation representing the total cost [tex]\( y \)[/tex] as a function of the number of hours [tex]\( x \)[/tex] used at the gym is:
[tex]\[ y = 3x + 1 \][/tex]
However, to make the equation more precise and to express the cost per hour as a fraction, we can write $3 as [tex]\( \frac{3}{1} \)[/tex] and then multiply both the numerator and the denominator by 4 to get [tex]\( \frac{3 \times 4}{1 \times 4} = \frac{12}{4} \)[/tex]. Simplifying the fraction [tex]\( \frac{12}{4} \)[/tex] gives us [tex]\( \frac{3}{4} \)[/tex]per hour.
Thus, the final slope-intercept form equation for the word problem is:
[tex]\[ y = \frac{3}{4}x + 1 \][/tex]
Help! Need help!
1. Justin is considering two websites for downloading music.The costs are detailed here.
Website 1: a yearly fee of $30 and $1.50 for each download
Website 2: $2 for each download
What is a system of equations to represent the costs for one year?
Express your equations in the form of y=mx+by=mx+b where x is the number of downloads for the year and y is the total cost for the year.
Website 1:
Website 2:
2. Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=4x−4y=−4x+4
a. consistent b. consistent and coincident c. inconsistent
equation for line parallel to 2x-3y+6=0, with the same y intercept
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
after 1 s = after 3 s = after 7 s =
Jay earns $5.90 per hour working at the ice cream parlor after school. He needs at least $236 for a stereo system. Choose the inequality that describes how many hours Jay must work to buy the stereo system.
21 is 60 percent of what number
What is the definition of percent??
Doug dives from a platform that is 7.5 meters above water. His dive takes him 2.1 meters below the surface of the water. How far does Doug's dive take him?
The ordered pair below is a solution to which equation? (2, 12) A.y=1/5x B.y=1/2x C. y = 2x D. y = 6x
Answer:
D. y = 6x
Step-by-step explanation:
In order to conclude which pair is a real solution to one of these equations, we need to evaluate the point in each equation.
Let:
[tex](x,y)=(2,12)[/tex]
So, this pair will be a solution if when evaluating the value of x=2 in the function the result is y=12.
For A.
[tex]y(x)=\frac{1}{5}x \\\\y(2)=\frac{2}{5} =0.4\neq12[/tex]
This pair is not a solution to this equation.
For B.
[tex]y(x)=\frac{1}{2}x\\\\y(2)=\frac{2}{2} =1 \neq 12[/tex]
This pair is not a solution to this equation.
For C.
[tex]y(x)=2x\\\\y(2)=2*2=4 \neq 12[/tex]
This pair is not a solution to this equation.
For D.
[tex]y(x)=6x\\\\y(2)=6*2=12[/tex]
This pair is a solution to this equation.
Select all that justify the following statement.
10 + x 12 = 12x + 10
a) commutative - addition
b) distributive
c) associative - multiplication
d) symmetric
e) commutative - multiplication
f) associative - addition
g) identity - addition
Answer:
The statement satisfied the expression 10 + x 12 = 12x + 10 is
Option (e) i.e commutative - multiplication and Option (a) i.e commutative - addition .
Step-by-step explanation:
Commutative Property
Let a, b be two numbers thus they satisfied the commutative property
i.e a + b = b + a
As given the expression.
10 + x ×12 = 12x + 10
First apply the Option (e) i.e Commutative - multiplication.
Thus expression becomes
10 + 12x = 12x + 10
Now apply the Option (a) i.e Commutative - addition.
Therefore the statement satisfied the expression 10 + x 12 = 12x + 10 is
Option (e) i.e commutative - multiplication and Option (a) i.e commutative - addition .
Make a mapping diagram for the relation.
{(–2, 2), (–1, –4), (0, –3), (2, 5)}
write a polynomial function in standard form with zeros at -3,-1, and 1
Answer:
Should be f(x) = x^3 + 3x^2 − x − 3 because this is written in standard form.
Step-by-step explanation:
what is the circumference this unit circle
The circumference of a unit circle is calculated using the formula C = 2πr. For a unit circle, where the radius (r) is 1, the circumference (C) is 2π, approximately 6.2832.
The Circumference of a Unit Circle
In mathematics, the circumference of a circle is the distance around its perimeter. For a unit circle, which is a circle with a radius of 1, the formula to calculate circumference is given by C = 2πr, where r is the radius.
Since the radius of a unit circle is 1, substituting in the formula gives us:
C = 2π(1) = 2π
Thus, the circumference of a unit circle is 2π, which is approximately 6.2832 when using the value of π ≈ 3.1416.
Solve the system of equations below by graphing them with a pencil and paper. Choose the correct ordered pair (b, u).
u = -b + 21
u = -2b + 30 ...?
change 50/16 into a mixed number .Reduce your answer to lowest terms a.48 3/16
b.3 1/25
c.3 1/8
d.4 7/8 ? ...?
HEELLLPPP ME?!?!?!? ANYONE?
Solve the system of equations and choose the correct ordered pair.
3x + 2y = 12
6x + 3y = 21
A. (4, 3)
B. (4, 0)
C. (2, 3)
D. (3, 2)
kenya picked 18 flowers from her garden. If 3/5 of flowers in her garden remain unpicked, how many flowers are still in her garden?
In algebra, why do you think that you are given many problems to solve that aren't really "real life" problems? For example, "Twice the sum of a number and 5 is 24. Find the number." ...?
Algebra problems may not seem like 'real-life' problems, but they help build a deeper understanding of mathematical concepts.
Explanation:Often, in algebra, you are given problems that may not seem like 'real-life' problems because they are designed to emphasize understanding the underlying concepts rather than simply executing a mathematical recipe. These problems aim to build a more meaningful understanding of the content by focusing on what the numbers represent and how they relate to each other. For example, in the problem 'Twice the sum of a number and 5 is 24. Find the number,' you can practice solving by setting up an equation and using algebraic manipulation to find the number.
"Which ranges describe the cluster in the scatter plot?
Choose exactly two answers that are correct.
A.between 8 and 10 years of age
B.between 32 and 72 pages read
C.between 10 and 12 years of age
D.between 32 and 38 pages read"
Answer:
A and C
Step-by-step explanation:
A.between 8 and 10 years of age
C.between 10 and 12 years of age
a country's population in 1995 was 56 million in 2002 it was 59 million. estimate the population in 2016
Answer:
69 420 911
Step-by-step explanation:
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations. graph of line going through ordered pairs (0, 300) and (450, 0)
which of the following is the sum of 3/18+2/18 reduced to lowest terms?
How did 25/10 gets simplified tho??
What is the value of X plez?
solve for x
5(2x - 1) = 6
A)x=1/10
B)X=11/10
C)X=1/2
what is 0.6(r 0.2)=1.8
the solution to the equation [tex]\(0.6(r - 0.2) = 1.8\) is \(r \approx 3.2\).[/tex]
To solve the equation 0.6(r - 0.2) = 1.8, we first distribute the 0.6 to the terms inside the parentheses:
0.6r - 0.6(0.2) = 1.8
0.6r - 0.12 = 1.8
Next, we add 0.12 to both sides of the equation to isolate 0.6r:
0.6r - 0.12 + 0.12 = 1.8 + 0.12
0.6r = 1.92
Now, to solve for r, we divide both sides of the equation by 0.6:
[tex]\[ \frac{0.6r}{0.6} = \frac{1.92}{0.6} \][/tex]
[tex]\[ r = \frac{1.92}{0.6} \][/tex]
[tex]\[ r \approx 3.2 \][/tex]
So, the solution to the equation [tex]\(0.6(r - 0.2) = 1.8\) is \(r \approx 3.2\).[/tex]
The probable question maybe:
solve the equation 0.6(r - 0.2) = 1.8
Which best describes the sides of any trapezoid?
A.
All sides are the same length.
B.
Only one pair of sides is parallel.
C.
Both pairs of opposite sides are parallel.
The answer is: only one pair of sides is parallel a.k.a b
What is 10 to the power of 3?