For the given problems we have:
1) The solution of the inequality is:
x ≤ 2
2) The absolute value equation has two solutions:
z= 2
z = -12
3) The correct matches are:
5y + 2 = 5y + 8 this has no solutions2*(y + 4) = 2y + 8 this has infinite solutions5y + 2 = 2y + 8 This has a single solution.How to solve the different operations?Remember that solving means to isolate the variable in one side of the expression.
1) We have the inequality:
-4x + 17 ≥ 9
-4x ≥ 9 - 17
x ≤ -8/-4
x ≤ 2
This is the solution of the inequality.
2) We have the absolute value function:
|5 + z| + 3 = 10
|5 + z| = 10 - 3 = 7
We can decompose this into:
5 + z = 7
5 + z = -7
Then the two solutions are:
z = 7 - 5 = 2
z = -7 - 5 = -12
3) The correct matches here are:
5y + 2 = 5y + 8 this has no solutions, these are parallel lines.2*(y + 4) = 2y + 8 this has infinite solutions (all real numbers).5y + 2 = 2y + 8 This has a single solution.Learn more about inequalities:
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A car uses 3 1/8 gallons of gasoline per hour when driving on the highway. How many gallons will it use after 4 2/3 hours? It will use _____________ gallons.
If the car uses 3 1/8 gallons per hour and the number of hours is 4 2/3, we can multiply both values to find the total amount of gallons used in this time.
First, we need to convert 3 1/8 and 4 2/3 into improper fractions:
[tex]\begin{gathered} 4\text{ }\frac{2}{3}=4+\frac{2}{3}=\frac{12}{3}+\frac{2}{3}=\frac{14}{3}\\ \\ 3\text{ }\frac{1}{8}=3+\frac{1}{8}=\frac{24}{8}+\frac{1}{8}=\frac{25}{8} \end{gathered}[/tex]Now, multiplying the values, we have:
[tex]\frac{25}{8}\cdot\frac{14}{3}=\frac{350}{24}=14.58[/tex]So the car will use 14.58 gallons.
A person from Switzerland consumes about 9.1 kilograms of chocolate per
year. A person from the United States consumes about 4.7 kilograms of
chocolate per year. How many times as much chocolate will a Swiss
person consume in one year than someone from the United States? Round
your final answer to the nearest tenths
Answer:
switzerland was the leading country in chocolate consumption per capita in 2017, with citizens eating nearly nine kilos of the sweet stuff in that year. World renowned for the chocolate they produce, it seems the Swiss themselves can’t get enough of the candy. Germany, the country’s neighbor, is equally addicted, importing the largest share of Swiss chocolate of all countries in the world.
Step-by-step explanation:
Answer: a swede would consume 1.9 times as much chocolate as an American.
Step-by-step explanation: 9.1 / 4.7 = 1.93617021. round to the nearest tenth = 1.9.
1.93617021 times 4.7 equals 9.1
Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches.
What is the probability that a randomly selected male is more than 70 inches tall?
There is a 0.5 percent probability that a randomly chosen male will be taller than 70 inches.
What is probability?Simply put, the 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 various outcomes. Statistics is the study of events that follow a probability distribution.So,
Mean height of the adults: μ = 70 inchesThe standard deviation: σ = 4 inchesThen, the formula will be:
Z = x-μ/σInsert the values in the formula as follows:
Z = x-μ/σZ = 70-70/4Z = 0Then,
0.5 is the p-value at z=0.P(x>70)=1-P(x<70)=1-0.5 = 0.5Therefore, there is a 0.5 percent probability that a randomly chosen male will be taller than 70 inches.
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The midpoint of AB is M(6, 3) . If the coordinates of A are (7, 4) , what are the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +7}{2}~~~ ,~~~ \cfrac{ y +4}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(6~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +7}{2}=6\implies x+7=12\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +4}{2}=3\implies y+4=6\implies \boxed{y=2}[/tex]
If you mix 3 oz of blue paint with 2 oz of yellow paint, and then decide to create 20 oz of the same mixture, how many ounces of yellow paint do you need?
tata:
• Blue paint (,: B,) 3
,• ellow poaint (
,• Mixture obtained ( ),O
,• Total mixture (), T
,• Total yellow paint (): , TY
Proportion f Y:
[tex]Y=\frac{2}{5}=0.4[/tex]TY:
[tex]TY=Y\cdot T=0.4\cdot20=8oz[/tex]nswer: 8oz
ummary:
0. We got the proportion of yellow paint in the mixture
,1. We multiply the proportion by the total mixture to know how many ounces of yellow paint is needed.
I need help on this problem can you help me?
The incenter is the center of a circumference that can be circumscribed inside the triangle. That means that the distance from the circumcenter to the sides of the triangle is the same. In this case, it means that:
[tex]NK=NL=NM[/tex]On the other hand, the segments from the circumcenter N to the vertices of the triangle are angle bisectors, and using that fact, it can be proven that the two triangles that form at each vertex from the angle bisectors are congruent. Then, we can also know that:
[tex]HK=HM[/tex]The congruence that cannot be deduced from the given information is:
[tex]NG\cong NJ[/tex]Translate the sentence into an equation
Nine times the sum of a number and 7 is equal to 5
Use the variable y for the unknown number
Hihuvhhhhhvhhhuuibvjj
Given expression is (a+b)^8 and we need to find the 5th term of this series.
Explanation -
The general binomial expression is given as
[tex](x+y)^n=^nC_0x^ny^0+^nC_1x^{n-1}y^1+^nC_2x^{n-2}y^2+............upto\text{ x}^0[/tex]So the given expression can be written as
[tex](a+b)^8=^8C_0a^8b^0+^8C_1a^7y^1+^8C_2a^6b^2+^8C_3a^5b^3+^8C_4a^4b^4+...[/tex]So the 5th term will be
[tex]\begin{gathered} 5th\text{ term = }^8C_4a^4b^4 \\ The\text{ general comb}\imaginaryI\text{nat}\imaginaryI\text{on formula }\imaginaryI\text{s = }^nC_r=\frac{n!}{(n-r)!r!} \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 5th\text{ term = }\frac{8!}{(8-4)!4!}a^4b^4 \\ 5th\text{ term = }\frac{8\times7\times6\times5}{4!}a^4b^4 \\ 5th\text{ term = }\frac{8\times7\times6\times5}{4\times3\times2\times1}a^4b^4=2\times7\times5\times a^4b^4=70a^4b^4=70(ab)^4 \end{gathered}[/tex]So the final answer is 70(ab)^4equations that are parallel to y=2x+11
y = 2x is the equation that is parallel to the given line in the question .
WHAT IS PARALLEL LINE ?If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.
CALCULATIONy = 2x + 11
choose a point which the line will pass through
(0,0)
using y = mx + b
m = 2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
[tex]y_{2} - y_{1} = m(x_{2} - x_{1} )[/tex]
y - 0 = 2x -0
y = 2x
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.44
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]
Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.
Show an equation
No, they will not have the same amount in their account at any point of time.
Given that:-
Money deposited by Rodney at the opening of savings account = $ 75
Money deposited by Rodney each month in the account = $ 40
Money deposited by Morgan at the opening of savings account = $ 50
Money deposited by Morgan each month in the account = $ 40
Let us imagine that they will have equal amount of money in their accounts at a particular point of time.
Let us consider x to be the number of months when they will have same amount of money in their account.
Hence, we can write,
75 + 40x = 50 + 40x
We can see that,
75 - 50 = 40x - 40x
25 = 0
But this is not possible.
Hence, they will never have the same amount of money in their accounts at a particular point of time.
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please help with this
Answer:
supplementary, not congruent.
Please answer question 8, I’d really appreciate it!!
Answer:
t = 8
Step-by-step explanation:
1. 2.5(t-2)-6 = 9 = 2.5t-5-6=9
2. add common terms = 2.5t - 11 = 9
3. add 11 on both sides to eliminate the 11
4. 2.5t= 20
5. 20/2.5 = 8
6. t = 8
In her notebook, Pia wrote these steps to construct a square inscribed in a circle:Use a compass and a straightedge to find chord LM, which is the perpendicular bisector of JK. Then, use a straightedge to draw the four chordsthat make up the square: JL, LK, KM, and MJ.Which instruction is Pia missing?
We want to draw chord LM such that it is a perpendicular bisector of line JK. The square would be drawn by joining lines JL, KL, KM and MJ
To achieve this, the daigram should look like the one shown below
This diagram is only possible if JK passes through the center of the circle. This means that JK is the diameter of the circle. Thus, the correct option is
B
Answer:
B
Step-by-step explanation:
Jonah studied z hours for a big test. Francesca studied a fourth as long. Write an algebraic expression for long Francesca studied.
The expression for study hours of Francesca will be ( Z + 4 ) hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jonah studied z hours for a big test. Francesca studied a fourth as long as Jonah studied.
The expression will be written as Francesca studied 4 hours more than Jonah.
Francesca's study time = ( Z + 4 ) hours
Therefore, the expression for study hours of Francesca will be ( Z + 4 ) hours.
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a department store buys 300 shirts at a cost of 3600 and sells them at a selling price of $20 each find the percent markup
We have the following:
To find the percent markup, we must calculate the profits, knowing that there are 300 shirts and they sell them for a total of $ 20
[tex]300\cdot20=6000[/tex]Now we subtract from what was initially spent and then divide by that same amount and multiplying by 100 we will know the percent markup
[tex]\frac{6000-3600}{3600}\cdot100=66.67\cong67[/tex]Which means that the percent markup is 67%
The following numbers represents the number of phone calls a class made in a given week:
125, 86, 142, 98, 126, 128, 90, 88, 98, 121
Use this data to find the following information. SHOW ALL WORK FOR CREDIT!
Mean: 110
e
Range:
Mode:
The mode and range of the given data is 98 and 42 respectively.
What is data?
Data, which can describe quantity, quality, fact, statistics, other fundamental units of meaning, or simply sequences of symbols that can be further interpreted, is a collection of discrete values that convey information in the pursuit of knowledge. A datum is a distinct state within a collection of data. Typically, data is arranged into structures like tables that give it additional context and meaning and can also be used as their own form of data in larger structures. It's possible to use data as variables in a computation. Data can represent both concrete measurements and abstract concepts. Data is used frequently in virtually every aspect of human organisational activity, including finance and science. Stock prices, crime rates, unemployment rates, literacy rates, and census data are a few examples of data sets.
Mode = 98 ( 98 occurs two times)
Range = 128-86=42
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Shandra owns a goldfish that currently weighs 0.50 ounces. With each inch that the goldfish grows, the goldfish weighs an additional0.15 ounces.PARTACreate an equation that Shandra can use to find the number of inches, r, it will take for the goldfish to weigh 1.1 ounces.PART BHow many more inches does the goldfish need to grow to weigh 1.1 ounces?inches
A.
The initial weight of the goldfish is 0.5 ounces.
Then, for each inch it grows, its weight increases by 0.15 ounces.
So, using the variable r to represent the number of inches it grew, we can write the following equation to determine the value of x for a weight of 1.1 ounces:
[tex]0.5+0.15r=1.1[/tex]B.
Solving the equation for r, we have:
[tex]\begin{gathered} 0.15r=1.1-0.5 \\ 0.15r=0.6 \\ r=\frac{0.6}{0.15} \\ r=4 \end{gathered}[/tex]It needs to grow 4 more inches.
A crane has a cable with a breaking strain of 6400 kg
measured to 2 significant figures.
It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
What is the
greatest number of crates that can safely be lifted
at one time without breaking the cable?
Some working must be shown.
The greatest number of crates that can safely be lifted at one time without breaking the cable is 71.
What is GCF?
The biggest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD). GCF is usually always utilised with fractions, which are frequently employed in daily life. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.
A crane has a cable with a breaking strain of 6400 kg measured to 2 significant figures. It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
We need to calculate the greatest number of crates that can safely be lifted at one time without breaking the cable.
According to the question,
It is given that, the breaking strain of the crane is 6,400 kilograms and each crate is 90 kilograms.
Thus, to know the number of crates (n) that can safely lift is equal to the weight of the crane is 6,400 kilograms divided by is 90 kilograms.
thus,
[tex]n=\frac{weight of the crane}{weight of each crate}\\ \\n=\frac{6400}{90}[/tex]
so, n= 71.111≈71
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Twice a number minus another numberis 8. Their sum is -2. Find thenumbers.
Set x and y to be the two numbers we need to find; then, according to the question,
[tex]\begin{gathered} 2x-y=8 \\ and \\ x+y=-2 \end{gathered}[/tex]Solve the system of equations as shown below
[tex]\begin{gathered} \Rightarrow y=2x-8 \\ \Rightarrow x+(2x-8)=-2 \\ \Rightarrow3x=6 \\ \Rightarrow x=2 \end{gathered}[/tex]Finding y,
[tex]\begin{gathered} x=2 \\ \Rightarrow y=2*2-8=-4 \\ \Rightarrow y=-4 \end{gathered}[/tex]Thus, the answer is 2 and -4, option E.Which is greater? -7/10 or -0.66?
Answer:
-7/10
Step-by-step explanation:
First, we obviously need to convert 0.66 into a fraction. Since -7/10 cannot be changed, we need to change AND simplify -0.66.
-0.66 is equal to -66/100, but we can still simplify this. We can divide the numerator and denominator by 2.
66 divided by 2 is 33.
100 divided by 2 is 50.
-33/50 CANNOT be simplified anymore.
So -7/10 _ -33/50. Which is greater?
-7/10 is closer to 0 on the number line. -33/50 isnt.
So -7/10 is the answer.
-7/10 > -0.66
The airport parking lot charges $2.00 to enter and $3.00 per hour after that. Carmen has N dollars and wants to be able to determine the maximum number of hours she can park. How can Carmen determine the length of time she can afford to park her car in the parking lot? Justify your answer.
The equation of the time she can afford to park her car is 2 + 3t = N
How to determine the time she can afford to park her carThe given parameters are
Entrance charge = $2.00Rate per hour = $3.00Assume she stays for t number of hours, the total charges would be
Total = Entrance charge + Rate per hour * Number of hours
This gives
Total = Entrance charge + Rate per hour * t
Substitute the known values in the above equation
So, we have
Total = 2 + 3t
From the question, she has N dollars
So, we have
2 + 3t = N
Hence, the expression of the description is 2 + 3t = N
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HELP INTERSECTIONS AND UNIONS!!
Given: A= {0,3,5,7,9,11,12}
B={-3,5,8,9,11,14}
C={-2,1,5,7}
1.) (A ∩ B) U C
2.) (B U C) ∩ A
The most appropriate choice for sets, union and intesrsection of set will be given by
1) (A ∩ B) U C = {-2, 1, 5, 7, 9, 11}
2) (B U C) ∩ A = {5, 7, 9, 11}
What is set and union and intersection of set?
Set is a well defined collection of distinct objects. Set can be empty as well as non empty.
Writing all the elements of two or more sets together in one set is known as union of sets.
Writing the common elements of two or more sets in one set is known as intersection of sets.
Given,
A= {0,3,5,7,9,11,12}
B={-3,5,8,9,11,14}
C={-2,1,5,7}
For 1)
(A ∩ B) = {5, 9, 11}
(A ∩ B) U C = {-2, 1, 5, 7, 9, 11}
For 2)
(B U C) = {-3, -2, 1, 5, 7, 8, 9, 11, 14}
(B U C) ∩ A = {5, 7, 9, 11}
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A local car dealership is trying to sell all of the cars that are on the lot. Currently, there are 725 cars on the lot, and thegeneral manager estimates that they will consistently sell 50 cars per week.1. Write and solve an inequality that can be used to find the number of full weeks, w, it will take for the number ofcars to be fewer than 125. Since w is the number of full or complete weeks, w = 1 means at the end of week 1.
Number of cars in the lot = 725 cars
W is the number of full or complete weeks
Also, 50 cars per week = 50w;
For every week, the cars will be reducing by 50;
(A) Hence , the inequality is given as;
[tex]725-50w<125[/tex][tex]\begin{gathered} 725-125<50w \\ 600<50w \\ \frac{600}{50}12 \end{gathered}[/tex]In how many ways can the digits in the number 9666111 be arranged?
========================================================
Explanation:
The unique digits are: 9, 6, 1
9 shows up once6 shows up three times1 shoes up three timesThere are 1+3+3 = 7 digits with the repeats mentioned. If we could somehow tell the 6's apart and the 1's apart, then we'd have 7! = 7*6*5*4*3*2*1 = 5040 different permutations.
But because we can't tell the 6's apart, nor the 1's apart, this means we have to divide by (3!*3!). Each 3! represents the number of times the 6's show up and same goes for the 1's.
So (5040)/(3!*3!) = 5040/(6*6) = 5040/36 = 140 is the number of ways to rearrange the digits
HURRY Consider the equation 3x3 + 14x2 – 14x + 60 = 0. The real solution is –6. What are the nonreal solutions?
Negative 2 i StartRoot 26 EndRoot, 2 i StartRoot 26 EndRoot.
4 minus 2 i StartRoot 26 EndRoot, 4 + 2 i StartRoot 26 EndRoot.
StartFraction negative 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction negative 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
StartFraction 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
The non-real solutions are (2 + i√26)/3 and (2 - i√26)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
x = -6
This gives
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
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the sum of two consecutive natural numbers is 313
Answer:
156 and 157
Step-by-step explanation:
John and Savanah are saving money to go on a trip to Mexico. They need at least $2,545 in order to go. John tutors English and Savanah works as a babysitter to raise money. John charges $15 per hour and Savanah charges $20 per hour. The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hours.. Write a set of constraints to model the problem, with x representing the number of hours John tutors and y representing the number of hours Savanah babysits
The group of restrictions used to simulate the issue includes
y<5x andy [tex]\geq[/tex] 40hours How to construct a set of restrictions to represent the issue:The issue includes the following information.
They require $2,545 split by John's and Savanah's hours. Savanah's hours are no more than five times John's. Savanah will babysit the kids for 40 hours.The limitations for modeling the problem are as follows: The gap between the number of hours Savanah has reserved and those that John has is no more than five times.
Savanah will provide child care for a minimum of 40 hours, but no longer than that, indicating that it is less than; as a result.
,y<5x
Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as
y ≥ 40 hours
The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.
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write an expression that can be used to find the value of x in the diagram below
since the angles are opposite by the vertex, we have that the expression to find the value of x is:
[tex]4x-1=55[/tex]and if we solve it, we obtain:
[tex]4x=54[/tex][tex]x=13.5[/tex]can u pls help me with this question
Answer:
Explanation:
eight of the bush when it was first planted int he garden = 12cm
After 2 weeks, its height = 120% of Height when it was planted.
[tex]=120\%\text{ of 12cm}[/tex]We solve for the result.
[tex]\begin{gathered} =\frac{120}{100}\times12 \\ =1.2\times12 \\ =14.4\operatorname{cm} \end{gathered}[/tex]The bush was 14.4cm tall after two weeks.