The expression is
4x + 4 < 9.2 + 8
4x < 9.2+8 - 4
4x < 9.2 + 4
4x < 13.2
x < 13.2/4
x < 3.3
So the lowest term is x < 3.3.
simplify 6n + 5(9 + 8n)
You have the following expression:
6n + 5(9 + 8n)
in order to simplify the previous expression, proceed as follow:
6n + 5(9 + 8n) apply distribution property
= 6n + 45 + 40n order like terms
= 6n + 40n + 45 simplify like terms
= 46n + 45
Hence, the simplified expression is 46n + 45
A quality inspector examines a sample of 40 strings of lights and finds that 4 are defective. What is the relative frequency of a string of lights being defective? Round your answer to 2 decimal places, if necessary.
Solution
- The formula for the relative frequency is given below:
[tex]\begin{gathered} rf=\frac{f}{n} \\ where, \\ f=\text{ The number of times the data occurred in an observation} \\ n=\text{ Total frequencies} \end{gathered}[/tex]- We have been given 4 defective lights and 40 total lights in the sample.
- Thus, we can find the relative frequency of a string of lights being defective:
[tex]\begin{gathered} f=4,n=40 \\ \\ rf=\frac{4}{40}=\frac{1}{10}=0.10\text{ \lparen To 2 decimal places\rparen} \end{gathered}[/tex]One month Jenny rented 2 movies and 3 video games for a total of $19. The next month she rented 4 movies and 8 video games for a total of $49. Find the rental cost for each movie and each video game.
Let be "m" the rental cost for each movie (in dollars) and "v" the rental cost for each video game (in dollars).
Based on the explanation given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}2m+3v=19 \\ 4m+8v=49\end{cases}[/tex]You can solve it using the Elimination method:
1. Multiply the first equation by -2.
2. Add the equations.
3. Solve for "v":
[tex]\begin{gathered} \begin{cases}-4m-6v=-38 \\ 4m+8v=49\end{cases} \\ ------------ \\ 2v=11 \\ \\ v=\frac{11}{2} \\ \\ v=5.5 \end{gathered}[/tex]4. Substitute the value of "v" into any original equation:
[tex]\begin{gathered} 2m+3v=19 \\ 2m+3(5.5)=19 \\ 2m=19-16.5 \\ \\ m=\frac{2.5}{2} \\ \\ m=1.25 \end{gathered}[/tex]The answer is:
- Cost for each movie: $1.25
- Cost for each video game: $5.5
In 2010, the population of a city was 105,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 6%. How much did the population grow from 2010 to 2015, to the nearest 100 people?
ANSWER:
The population increased by 8,400 people making the total population of 113,400 people
STEP-BY-STEP EXPLANATION:
In this case we must add the value of the current population and then multiply that population by the percentage of increase, just like that:
[tex]105000+105000\cdot\frac{8}{100}=105000+8400=113400[/tex]Which means that the population increased between 2010 to 2015 by 8,400 people, making the total population of 113,400 people.
Tessa had in her checking account. She paid her cable/internet bill for . She deposited from her part-time job before writing a check for to pay her credit card bill. What is Tessa's account balance?
Explanation:
Tessa originally had $110 in her account, we need to find the account balance (the final amount in her account) after all of her deposits and expenses.
We start by considering that she paid $75 for the cable/internet bill, we discount 75 to the original amount of 110:
[tex]110-75=35[/tex]Then, she had a deposit of $50 from her part-time job, therefore, this amount was added to her account, now we add 50 to the 35 that she had left:
[tex]35+50=85[/tex]Finally, she wrote a check for $85 to pay her credit card, thus, this amount was discounted from the previous $85:
[tex]85-85=0[/tex]In the end, she has $0 left, and the account balance is 0 dollars.
Answer: 0 dollars.
solve the system of equations using the elimation method. show your work. make sure to express your solution as an ordered pair
Given the system of equations:
[tex]\begin{gathered} 6x+4y=7\rightarrow(1) \\ 6x+2y=5\rightarrow(2) \end{gathered}[/tex]Subtract equation (2) from equation (1):
So,
[tex]\begin{gathered} (6x+4y)-(6x+2y)=7-5 \\ 4y-2y=2 \\ 2y=2 \\ y=\frac{2}{2} \\ y=1 \end{gathered}[/tex]substitute with y into equation 1 to find x:
[tex]\begin{gathered} 6x+4=7 \\ 6x=7-4 \\ 6x=3 \\ \\ x=\frac{3}{6} \\ \\ x=\frac{1}{2} \end{gathered}[/tex]So, the answer will be:
x = 1/2 y = 1
( x, y ) = ( 1/2 , 1 )
See the following picture:
solve a = d+c ÷b for d
Assuming the question is:
[tex]a=d+\frac{c}{b}[/tex]we need to solve for d.
We keep "d" to one side and simplify the other side for a formula for d. Shown below:
[tex]\begin{gathered} a=d+\frac{c}{b} \\ d=a-\frac{c}{b} \\ d=\frac{ab-c}{b} \end{gathered}[/tex]Use the remainder theorem to find P (1) for P(x) = -2x⁴+3x³ + 6x² -7. Specifically, give the quotient and the remainder for the associated division and the value of P (1).
Step 1
Given;
[tex]P(x)=-2x^4+3x^3+6x^2-7[/tex]Required; To find P(1)
Step 2
Set x=1
[tex]\begin{gathered} P(1)=-2(1)^4+3(1)^3+6(1)^2-7 \\ =-2\cdot \:1+3\left(1\right)^3+6\left(1\right)^2-7 \\ =-2\cdot \:1+3\cdot \:1+6\cdot \:1-7 \\ =-2+3\cdot \:1+6\cdot \:1-7 \\ =-2+3+6\cdot \:1-7 \\ =-2+3+6-7 \\ =0 \end{gathered}[/tex]Using the factor remainder theorem;
Hence;
[tex]\begin{gathered} Quotient=-2x^3+x^2+7x+7 \\ Remainder=0 \\ P(1)=0 \end{gathered}[/tex]Find the probability that the person had an iPod given that they didnot have an iPhone.
The intersection of the second column and the third row serves as the numerator: 13.
The total number of people who has no iPhone: 22.
To obtain the probability, divide the obtained intersection by the total number of people.
[tex]P=\frac{13}{22}[/tex]Therefore, the last option is correct.
Combining like terms 10 + 8a - 5 - 10a + 14 -7a
Remember that we add and substract like terms. This means that we add the terms with a (in this case 8a-10a-7a=-9a) and the terms with no variable (10-5-14=19).
Please provide deep explanation, so i can understand and learn. Thank youI dont think its asking for a definitive answer but a way on how you could find the thickness of 2 sheets.
Given that:
- The box contains 5 reams of paper.
- One ream of paper is 500 sheets of paper.
Let be "x" the thickness of a ream of paper.
Knowing the number of sheets that one ream of paper contains, you can determine that the thickness of one sheet of paper is:
[tex]\frac{x}{500}[/tex]In this case, you need to estimate the thickness of 2 sheets of paper. Therefore, assuming that all the sheets have the same thickness, you need to multiply the thickness of one sheet of paper by 2:
[tex]2\cdot\frac{x}{500}[/tex]Hence, the answer is: You could divide the thickness of one ream of paper by the number of sheets of paper a ream of paper has, in order to find the thickness of one sheet of paper, and then multiply the result by 2.
Triangle ABC above is isosceles with AB=AC and BC=48. The ratio of DE to DF is 5 : 7. What is the length of DC?
The triangle ABC is an isosceles with AB=AC.
BC=48
Now given that
DE:DF=5:7.
Since DE is perpendicular to AB and DF is perpendicular to AC, therefore,
BD:DC=5:7
It happens because as DE:DF=5:7, the ratio of the area of the two reight angle triangles is also 5:7.
So, their base must be in the same ration.
Now, two sides are in same ratio, by default, their third sides i.e., BD and DC have the ratio 5:
Since, BC=48, therefore,
[tex]\begin{gathered} DC=\frac{7}{12}\times48 \\ =28 \end{gathered}[/tex]Hence, the correct option is (D).
Which expression is equivalent to(1.794 ?А4 + 1.7B4x 1.7с1.7 + 4 + 1.7 + 4 + 1.7 + 4 + 1.7 + 4D1.7 x 1.7 x 1.7 x 1.7
Question 5 of 8What is the value of the rational expression below when xis equal to 4?X-12X-8
By substituting the value 4 into the given expression, we get
[tex]\frac{4-12}{4-8}[/tex]then the answer is
[tex]\frac{-8}{-4}=2[/tex]that is, the solution is 2.
Find three solutions to each linear equation. x+y=8
greaSolution
We have this equation
x+y=8
Three possible solutions are:
x=2, y=6
x=4, y=4
x=6, y=2
i need help on the last option C. would it be “upward” or “downward”?
Answer:
Explanation
The graph is a straight line, it is upward, and it is shown in option
Simplify each expression and show as much work as possible.
Simplify:
(1)
[tex]4w^2+7w^2+7z^2[/tex](2)
[tex]15w-6w+14w^2[/tex]Explanation:
(1)
take common
[tex]w^2[/tex][tex]\begin{gathered} 4w^2+7w^2+7z^2 \\ =w^2(4+7)+7z^2 \\ =11w^2+7z^2 \end{gathered}[/tex](2)
take
[tex]w[/tex]common from the given equation
[tex]\begin{gathered} 15w-6w+14w^2 \\ =w(15-6)+14w^2 \\ =9w+14w^2 \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} 4w^2+7w^2+7z^2=11w^2+7z^2 \\ 15w-6w+14w^2=9w+14w^2 \end{gathered}[/tex]What is the perimeter of a rectangle that has a length of 13x + 9 and a width of 7x + 4? *
Given the rectangle that has length of ( 13x + 9 ) and a width of (7x + 4)
the perimeter of the rectangle = 2 * ( length + width )
So,
The perimeter = 2 * [ (13x + 9) + ( 7x + 4) ]
= 2 * ( 13x + 9 + 7x + 4)
= 2 * ( 20x + 13 )
= 2 * 20x + 2 * 13
= 40x + 26
So, the perimeter of the rectangle = 40x + 26
[tex](2 \sqrt{2 + 5i)} (5 \sqrt{2 - 2i)} [/tex]what is the product
Answer:
[tex]30+21i\sqrt[]{2}[/tex]Explanation:
Let's go ahead and find the product as shown below;
[tex](2\sqrt[]{2}+5i)(5\sqrt[]{2}-2i)[/tex][tex]=(2\sqrt[]{2}\times5\sqrt[]{2})+(2\sqrt[]{2}(-2i))+(5i\times5\sqrt[]{2})+(5i\times(-2i))[/tex][tex]=(10\times2)+(-4i\sqrt[]{2})+(25i\sqrt[]{2})+(-10i^2)[/tex]Note that i^2 = -1, so we'll have;
[tex]=20-4i\sqrt[]{2}+25i\sqrt[]{2}-10(-1)[/tex][tex]\begin{gathered} =20-4i\sqrt[]{2}+25i\sqrt[]{2}+10 \\ =30+21i\sqrt[]{2} \end{gathered}[/tex]which ordered pair is a solution of the equation? y= -2x - 5choose 1 answerA: only (1,7) B: only (2,-7)C: both (1,7) and (2,-7)D: Neither
if we replace x by 1 we get
[tex]y=-2\cdot1-5=-7[/tex]so (1,7) is not a solution
if we replace x by 2. We get:
[tex]y=-2\cdot2-5=-9[/tex]so (2,-7) is not a solution.
So neither is the correct option
Square ABCD has vertices A(-8,-8), B(-8, 1), C(1, 1), and D(1, -8). Findthe length of one side of square ABCD. Round your answer to thenearest tenth if necessary.
Answer:
9 units.
Step-by-step explanation:
In a square, all sides have the same length. So in this question, the distance between any of these two points is the length of a side.
Distance between two points.
Point A(x1, y1)
Point B(x2,y2)
The distance is given by:
[tex]D=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]In this question:
I am going to draw the square
The length of the side can be the distance between any of these points:
A and B, B and C, C and D or A and D.
I am going to use A and D.
A(-8,-8)
D(1,-8)
[tex]D=\sqrt{(1-(-8))^2+(-8-(-8))^2}=\sqrt{(9)^2+(0)^2}=\sqrt{81}=9[/tex]The length of one side is of 9 units.9 units.
Challenge problem (opinional)
First, let's start by findind the slope
Pick any two point from x and its correspondance y
I will choose;
(4, 0) and (8, 3)
To find the slope, we will use the formula;
slope(m) = y₂ - y₁ /x₂ - x₁
x₁ = 4 y₁ = 0 x₂ = 8 y₂ = 3
substituting into the formula;
slope (m) = 3-0 / 8-4
slope(m) = 3/4
slope(m) = 0.75
We can find the y intercept using the formula;
y= mx + b
where b is the intercept
substuting any of the point (x,y) and slope(m) then solve for b
I will choose the point (4, 0)
slope(m) = 0.75
substituting the values into the formula;
0 = (0.75 )(4) + b
0= 3 + b
subtract 3 from both-side of the equation
-3 = b
b= -3
The y-int. is -3
We can form our equation using;
y = mx + b
m= 0.75 or 3/4
b = -3
substituting into the formula;
y = 0.75x -3
or
y= 3/4 x - 3
+ b
Question 8 (2 points)Given the table below, determine the probability of selecting a female student istaking physics. Round your answer to the nearest hundredth,MalesFemalesBiology6070Chemistry5560PhysicsTotal175175Your Answer:Answer
I will assume the general table given in the problem.
-------------------------------------------------------------------------------------
Let's draw the table,
Since all the information and total is given, except physics, let us calculate the two blanks in the table.
So, the completed table is,
We want the probability of selecting a female student taking physics.
For that, we need the number of female physics students and the total number of students.
From the table, we see that,
Female Physics students = 45
Total number of students = 175 + 175 = 350
Thus,
The probability of selecting a female student taking physics is 45/350
Or,
0.12857
Rounding to the nearest hundredth (2 decimal places), the answer is
0.13
Answer0.13Write the slope of 2x+y=-3
To find the slope of this linear equation, we can rewrite this into the slope-intercept form, as follows:
[tex]2x+y=-3\Rightarrow y=-3-2x\Rightarrow y=-2x-3[/tex]In the slope-intercept form, we can say that the slope for the line is m = -2.
Therefore, the slope for this line is m = -2.
We have to remember that the slope-intercept form of the line is:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept of the line.
How do you find the volume of a cube ?A) You find the volume of a cube by multiplying its length by its width by its height ?B) You find the volume of a cube by multiplying its length b its width and adding its height ?C) You find the volume of a cube by adding its width to its height ?D) You find the volume of a cube by subtracting its length from its width and adding its height ?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define the volume of a cube
[tex]Volume=a^3[/tex][tex]\begin{gathered} Recall\text{ that:} \\ length=width=height=a \end{gathered}[/tex]Hence, answer is:
"You find the volume of a cube by multiplying its length by its width by its height"
A cone with diameter 5 inches and height 7.5 inches is shown. 7.5 in 5 in Enter the volume of the cone, in cubic inches. Round your answer to the nearest hundredth.
We are asked to determine the volume of a cone. To do that we will use the following formula:
[tex]V=\frac{1}{3}(\pi r^2)h[/tex]Where "r" is the radius and "h" is the height. Since the diameter is twice the radius that means that r = 5/2. Replacing the values we get:
[tex]V=\frac{1}{3}(\pi(\frac{5}{2}in)^2)(7.5in)[/tex]Solving the operations:
[tex]V=49.09in^3[/tex]Volume & Surface Area, Area of SectorsBA = 6.5 cm
Explanation:
BA = radius
Radius = 6.5cm
< ABC = 23 degrees
pi = 3.14
[tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360}\cdot\text{ }\pi\cdot r^2 \\ \text{Area of a sector = }\frac{23}{360}\text{ x 3.14 x 6.5 x 6.5} \\ \text{Area of a sector = }\frac{23\text{ x 3}.14\text{ x 6.5 x 6.5}}{360} \\ \text{Area of a sector = }\frac{3051.295}{360} \\ \text{Area of a sector = 8.5 cm}^2 \end{gathered}[/tex]Therefore, the area of a sector is 8.5 square cm
14.6÷0.7......solutions and reasoning
Given:
an expression is given as 14.6 ÷ 0.7
Find:
we have to evaluate the given expression.
Explanation:
Since we can write 14.6 as 146/10 and 0.7 as 7/10,
we will evaluate the given expression as follows
[tex]14.6÷0.7=\frac{14.6}{0.7}=\frac{\frac{146}{10}}{\frac{7}{10}}=\frac{146}{7}=20.8571[/tex]Therefore, 14.6 ÷ 0.7 = 20.8571
Sets B and C are subsets of the universal set U.These sets are defined as follows.U={f,m,q, r, s,y}B={f.q,s,y}C={f.ris)Find the following sets.Write your answer in roster form or as Ø.(a) (BAC)' = 0....O х$?(b) B'UC = 0
SOLUTION:
We are given the sets;
[tex]\begin{gathered} U=\lbrace f,m,q,r,s,y\rbrace \\ B=\lbrace f,q,s,y\rbrace \\ C=\lbrace f,r,s\rbrace \\ Clearly,B,C\subseteq U \end{gathered}[/tex]We want to find the following;
[tex](B\cap C)^{\prime}[/tex]This means what is not in the intersection set but in the universal set,
The intersection set is;
[tex]\begin{gathered} B\cap C=\lbrace f,s\rbrace \\ thus; \\ (B\cap C)^{\prime}=\lbrace m,q,r,y\rbrace \end{gathered}[/tex][tex]\begin{gathered} B\cap C=\lbrace f,s\rbrace \\ thus; \\ (B\cap C)^{\prime}=\lbrace m,q,r,y\rbrace \end{gathered}[/tex]We also want to find;
[tex]B^{\prime}\cup C[/tex]This means the union of B complement joined with C, neglecting repititions.
We have;
[tex]\begin{gathered} B^{\prime}=\lbrace m,r\rbrace \\ C=\lbrace f,r,s\rbrace \\ thus; \\ B^{\prime}\cup C=\lbrace f,m,r,s\rbrace \end{gathered}[/tex]2/5Solving a word problem using a system oflinear equations of the form Ax + By = C
Let's set x for each movie
Set y for each video.
Now, we have the next given information:
One month Latoya rented 2 movies and 3 video games.
We can write the next equation:
2x + 3y = 19
Also, the next she rented 4 movies and 8 video games.
We can write the next equation:
4x + 8y = 49
With both equations with the same variables, we have a system of equations:
1) 2x + 3y = 19
2) 4x + 8y = 49
Solve the system of equations using the elimination method.
First, multiply the first function by 4 and then multiply the second function by 2.
4(2x + 3y = 19)
8x +12y =76
and
2(4x + 8y = 49)
8x + 16y = 98
Subtract both functions:
[tex]\begin{gathered} 8x+12y=76 \\ 8x+16y=98 \\ --------------- \\ (8x-8x)+(12y-16y)=(76-98) \\ 0-4y=-22 \\ \text{Solve for y:} \\ y=\frac{-22}{-4} \\ y=5.5 \end{gathered}[/tex]With the y value, we can replace it on the first function:
[tex]\begin{gathered} 2x+3y=19 \\ 2x+3(5.5)=19 \\ \text{Solve for x:} \\ 2x+16.5=19 \\ 2x=2.5 \\ x=\frac{2.5}{2} \\ x=1.25 \end{gathered}[/tex]Hence:
The rental cost for each movie is $1.25
The rental cost for each video game is $5.5