The sum equivalent to 7√28x⁶+4√7x⁶ is :
18√7x⁶ .
Solution:Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given ,7√28x⁶+4√7x⁶,
To find sum in simplest form ;
7√28x⁶+4√7x⁶
By splitting to factors,
= 7√(7*4)x⁶+4√7x⁶
= 7*2√7x⁶+4√7x⁶
= 14√7x⁶+4√7x⁶
By factoring out like terms,
= 2√7x⁶(7+2)
= 2√7x⁶(9)
= 18√7x⁶
Therefore sum is = 18√7x⁶.
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given the following expressions1. -5/8+3/52. 1/2+ √23. (√5)×(√5)4. 3×(√49)which expression(s) will result in an irrational number.(1) only 2(2) only 3(3) 1,3,4(4) 2,3,4
1) Only 2
1) Examining the expressions we have
1. -5/8+3/5 =-1/40 Rational Expression
2. 1/2+ √2 Irrational Expression
3.(√5)×(√5)= 5 Rational Expression
4. 3×(√49) = 21 Rational Expression
2) Since √2 is an irrational number √2 = 1.4142.... non-periodic and infinite number, and number added to it will yield an irrational number.
3) So the answer is 1) Only 2
simplify 4√(384.5)³ using logarithm
After simplification of 4√(384.5)³ using logarithm, the resulting answer is 30158.13684.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number. When measuring the relative change of a value rather than its absolute difference, logarithmic scales are helpful. Moreover, logarithmic scales are used to compress large-scale scientific data because the logarithmic function log(x) grows very slowly for large x. Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular types of logarithms.So, 4√(384.5)³ using logarithm:
(Refer to the image attached below for calculations.)= 30158.13684Therefore, after simplification of 4√(384.5)³ using logarithm, the resulting answer is 30158.13684.
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) assembly comprises 769 team members. given that tmm operates two shifts a day, and assembly has 353 stations, what is the proportion of team members not assigned to one of the stations?
Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769
Proportion means a share from total set being discussed.
Data from the given case:
- The assembly has 769 team members.
- The assembly has 353 stations
- At each station, there are 2 shifts operations.
Assuming that 1 person is assigned to 1 shift operation, then there will:
353 x 2 = 706 person assigned.
The remaining team members that not assigned is:
769 - 706 = 63 person.
Therefore, the share or the proportion of unassigned team members is:
63/769
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Which graph shows y=3⌊x⌋−4? Responses Graph of the function f open argument x close argument equals greatest integer on a coordinate plane. The horizontal x axis ranges from negative 10 to 10. The vertical f of x axis ranges from negative 10 to 10. The graph is a step function with 7 vertical line segments. Each line segment is one unit long, with a closed point on the left side and an open point on the right side. Moving left to right, each line segment is shifted to the right one unit and up one unit, compared to the line segment before it. The endpoints of the first three line segments are as follows. Segment one. Begin ordered pair negative 2 comma negative 10 end ordered pair and begin ordered pair negative 1 comma negative 10. Segment two. Begin ordered pair negative 1 comma negative 7 end ordered pair and begin ordered pair 0 comma negative 7 end ordered pair. Segment three. Begin ordered pair 0 comma negative 4 end ordered and 1 comma negative 4 end ordered pair. The pattern continues with the last line segment at an endpoint. Image with alt text: Graph of the function f open argument x close argument equals greatest integer on a coordinate plane. The horizontal x axis ranges from negative 10 to 10. The vertical f of x axis ranges from negative 10 to 10. The graph is a step function with 7 vertical line segments. Each line segment is one unit long, with a closed point on the left side and an open point on the right side. Moving left to right, each line segment is shifted to the right one unit and up one unit, compared to the line segment before it. The endpoints of the first three line segments are as follows. Segment one. Begin ordered pair negative 2 comma negative 10 end ordered pair and begin ordered pair negative 1 comma negative 10. Segment two. Begin ordered pair negative 1 comma negative 7 end ordered pair and begin ordered pair 0 comma negative 7 end ordered pair. Segment three. Begin ordered pair 0 comma negative 4 end ordered and 1 comma negative 4 end ordered pair.
The graph for the given equation is plotted below.
The given equation is y=3x-4.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Put x=0, 1, 2, 3, 4,....in the given equation and solve for y
When x=0, y=-4
When x=1, y=-1
When x=2, y=2
When x=3, y=5
Plot the coordinates (0, -4), (1, -1), (2, 2) and (3, 5) on the graph.
Therefore, the graph for the given equation is plotted below.
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Solve −5d +2≥7 or 2d −2>8
Answer:
for the first one: d ≥ 1
for the second one: d > 5
What are the vertex and range of y = |x + 3| + 2?
a (−3, 2); 2 ≤ y < ∞
b (−3, 2); −∞ < y < ∞
c (0, 5); 2 ≤ y < ∞
d (0, 5); −∞ < y < ∞
The vertex of the equation is (-3, 2). And the range will be the set of all real numbers equal to or larger than 2, written as:
y ≥ 2.
What is the vertex and range of the absolute value function?
For an absolute value function of the form:
y = |x - a| + b
The vertex is a the point (a, b).
And the range (the set of the possible values of y that we can get with the function) will be the set of all real values equal or larger than b.
In this case, the absolute value function is:
y = |x + 3| + 2
Comparing it with the general one, we can see that the vertex is (-3, 2)
And then the range is y ≥ 2.
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ABCD - FECG B 5 E 6 100° 5 A 60° С 4 120° G w D W = ? 1°
From the figure, draw from D parallel to AB.
Calculate angle D from triangle DWC = 180 - (90+60) = 180 - 150 = 30
Angle D = 30
Angle W = 90 + 30 = 120
Final answer W = 120
You deposit $400 in an account that earns 3. 5% interest compounded annually. What is the account balance after 2 years?
Account balance after 2 years $441.
Based on the given condition, here the details:
P = $400
r = 5 % = 0.05
n = 1
t = 2
Formulate and substitute all above:
F = P · (1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]
F = 400. 1 + [tex]\frac{0.05}{1}[/tex])²
F = $441
From this as general, account balance is:
A checkbook, a savings account, or an investment account, for example, has a balance that shows how much money is available in the account. This is also called the current account value. The current value of account balances is shown by financial institutions on both paper statements and online tools.
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As a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 62 Second number: 52
We will multiply by 26 / 31 in the first number to get second number for fraction in simplest form.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
In the fraction,
The first number = 62
The second number = 52
Let the number which can be multiply by the fraction = x
Since, The given condition is,
Multiply the first number by to get the second number.
So, We can formulate;
⇒ 62 × x = 52
Solve for x, as;
⇒ 62 × x = 52
⇒ 62x = 52
Divide by 62, we get;
⇒ x = 52 / 62
Multiply and divide by 2;
⇒ x = 26 / 31
Therefore,
We will multiply by the number 26 / 31 in the first number to get second number for fraction in simplest form.
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Which expression is equivalent to 6(−3.1y − 10.8)?
−18.6y − 64.8
−18.6y − 10.8
2.9y − 4.8
2.9y − 10.8
Answer:
The answer for the question is = -18.6y - 64.8
Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
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Please help!
4|x+7| < 8
3
so this is a
You also will not know precisely how many sentences will appear in the random paragraph. But some piano roll artists made a name with pieces that could not possibly be played by an precise individual. Most of his research deal with difficult meters and polyrhythms. Many include distinct voices enjoying the identical line at different tempos, usually in odd ratios. On top of this, most of the traces themselves tend to be highly dissonant and exhausting to actually play. Someday we might come nose to nose with pure house, that could presumably be a nothingness waiting to be filled.
(01.06 MC)
Ray IL bisects angle HIJ. If mzHIL = (6x - 7)° and mzJIL = (5x + 4)°, what is mzJIL?
118°
59°
44°
11°
Option C, 59° is correct answer, The angle JIL is equal to 59 degree.
What is angle?
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.
Given information in the question,
∠HIL = (6x-7)°
∠JIL = (5x+4)°
The ray IL bisects the ∠HIJ
Since, IL bisects angle HIJ then, angle HIL = angle JIL
So,
6x - 7 = 5x + 4
x = 11
Putting the value of x in given value of JIL to get the angle JIL
∠JIL = (6x-7)°
∠JIL = (6(11)-7)°
∠JIL = 59°
Therefore angle JIL is equal to 59 degrees.
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Find the mean for n = 200 and p = 0.24 when the conditions for the binomial distribution are met.
The mean value of expected value for a binomial distribution is given by the next formula:
[tex]\mu_x=n\cdot p[/tex]Where n is the number of trials and p is the probability of success. So, using the given data:
[tex]\begin{gathered} \mu_x=200\cdot0.24 \\ \mu_x=48 \end{gathered}[/tex]So the expected value or mean is 48
I need help with the question below please:A painter must thin some paint for use in a sprayer. If the recommended rate is 1/9 pint of water per gallon of paint, how many total gallons will there be after thinning 36 gallons of paint?
The cost of entering a carnival and riding rides is given by the linear equation, c(r) = 1.25r + 6.00, where c(r) is the total cost of attending the carnival and r is the number of rides. the slope of the linear equation represents the response area .
Answer: Cost per rides
Step-by-step explanation:
For the figure below, give the following
Answer:
Step-by-step explanation:
B
The following are daily customer numbers at an outerwear store. You've calculated themedian number of customers for the first six days of the week:Monday Tuesday Wednesday Thursday Friday Saturday Sunday175132A. IncreaseB. DecreaseC. Stay the same121129145160Q. If the store has 173 visitors on Sunday, will the median increase, decrease, or stay thesame?
Answer:
[tex]A\text{ : Increase}[/tex]Explanation:
Here, we want to deduce the median change
The median is a measure of central tendency that represents the middle number is a set of numerical observations
Firstly, let us get the previous median
We start by sorting the numbers from bottom to top
We have that as:
121,129,132,145,160,175
Since the count of observations is even, we have the median as the average of the two mid-values
We have that as:
[tex]\frac{132+145}{2}\text{ = 138.5}[/tex]Adding the last value, the set becomes
121,129,132,145,160,173,175
In this case, the median value would be 145 which shows an increase in the value of the median
Answer:
A. Increase
Step-by-step explanation:
I took the
The latest crime statistics in the united states suggest that eighteen-to-twenty-four-year-olds make up about – percent of the population but account for – percent of criminal arrests, while people sixty-five and older make up more than – percent of the population but account for less than – percent of arrests
Using concepts of statistics, we got 7% people are from age 18-24,and 15% for criminal arrests,65 and older are in 13% population and cover less than 1% crime rate.
The topic of crime in the United States is very large, technically covering any action that is punishable under a state or federal law. Any analysis of the topic requires division into further sub-categories. One common way to do this is by limiting analysis to crimes involving jail time (i.e. misdemeanors and felonies, which generally differ via the length of jail time involved), then differentiate between violent crimes or property crimes. Violent crimes are described as offenses which involve force or the threat of force, while property crime majorly includes offences involving the taking of money or property, but where there is not any force or threat of force against the victims. Property crimes are outnumbering violent crimes in the U.S. in 2020, numbering 6.45 million and 1.31 million respectively. Larceny was the actually most common property crime with 4.6 million incidents, while the aggravated assaults accounted for around two thirds of violent crimes.
Hence, percentage of people whose age is in between 18-24 is 7%,
people from age 18-24 engaged in illegal work=15%,
percentage of people whose age is 65 or more than =13%,
people involved in crime having age more than or equal to 65=1%
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How do I know when to subtract or add or divide when it comes to the end of the solution?
Given a rectangular peice of paper
Length = 34 cm
Width = 16 cm
So, the area of the rectangle = 34 x 16 = 544 cm²
Two semicircles cut out of it
The diameter of the circle = d = 16 cm
So, the radius of the circle = r = d/2 = 8 cm
The area of the two semicircles = area of the complete circle
so, the area of the circle = πr² = 3.14 x 8² = 200.96 cm²
So, the area of the remaining paper = area of the rectangle - area of the circle
= 544 - 200.96 = 343.04 cm²
So, the answer will be Area = 343.04 cm²
At a high school, students can choose between three art electives, four history electives, and five computer electives.
Fach student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
O
7C2
1202
С
.?
122
O (G) 4401)
12Cz
12P2
Mark this and return
Save and Exit
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Submit
Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
As given in the question,
Number of art electives students = 3
Number of history electives students = 4
Number of computer electives students = 5
Choosing an art electives students = ³C₁
Choosing an history electives students = ⁴C₁
Expression represents the probability that a student chooses an art elective and a history elective
= (³C₁⁴C₁) / ¹²C₂
Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
The complete question is:
At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
a. ⁷C₂ / ¹²C₂
b. ⁷P₂ / ¹²P₂
c. (³C₁⁴C₁) / ¹²C₂
d. (³P₁⁴P₁) / ¹²P₂
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A tree initially measured 18 feet tall. Over the next 3½ years, it grew to a final height of 35½ feet. During those 3½ years, what was the average yearly growth rate of the height of the tree?
Answer:
The average yearly growth o
Explanation:
Given that the tree grew from 18 ft 35 1/2 feet in 3 1/2 years.
The growth within these years is:
35 1/2 - 18
= 35.5 - 18
= 17.5
Now, this averages:
17.5/3.5 (3.5 is the number of years)
= 5
The average is 5 ft per year
Find an
an equation for the perpendicular bisector of the line segment whose
endpoints are (–4,3) and (−8,—3).
Answer:
y = (-2/3)x + 4
Step-by-step explanation:
Use identities to find tan, csc, sec, and cot. Where necessary, rationalize denominators
We are given:
[tex]sin\text{ }\theta=\frac{3}{5},cos\text{ }\theta=\frac{4}{5}[/tex]The tangent is defined as the ratio of the sine and the cosine:
[tex]tan\text{ }\theta=\frac{sin\text{ }\theta}{cos\text{ }\theta}[/tex]Calculating:
[tex]\begin{gathered} tan\text{ }\theta=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{5}\cdot\frac{5}{4} \\ \\ tan\text{ \theta}=\frac{3}{4} \end{gathered}[/tex]The cotangent is the reciprocal of the tangent:
[tex]\begin{gathered} \cot\theta=\frac{1}{\tan\theta} \\ \\ \cot\theta=\frac{1}{\frac{3}{4}}=\frac{4}{3} \end{gathered}[/tex]The secant is the reciprocal of the cosine:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{1}{\frac{4}{5}} \\ \\ \sec\theta=\frac{5}{4} \end{gathered}[/tex]The cosecant is the reciprocal of the sine:
[tex]\begin{gathered} \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{3}{5}} \\ \\ \csc\theta=\frac{5}{3} \end{gathered}[/tex]how many elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements? how many ways are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each? (assume that no student can have more than one major.) how many ways are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6?
a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.
b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.
c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.
The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set B or including more sets
For the first problem, the sets contain:
n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0
So, n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)
= 10 +15+25-0-0-0-0-0
= 50
For the second problem, since no student can have more than one major.
So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)
As we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17
So , (A∪B∪C∪D∪E∪F∪G) = 31+88+19+11+41+22+17= 229
For the third problem, we have
n(A)=5
n(B)=3
n(C)=2
n(D)=7
n(E)=6
So, the number of elements will be (A∪B∪C∪D∪E) = 5+3+2+7+6 =23
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f(x)=6x^2+11 inverse
Answer:
√6(x−11)/6
Step-by-step explanation:
f^−1(x)=√6(x−11)/6
Hey , I have a quick question about a Homework in math I got confused on how to solve the listed to formula [tex] \frac{x - 3}{2} - 4 \ \textless \ \frac{x}{3} [/tex]
Solution
- The question would like us to solve the following
[tex]\frac{x-3}{2}-4<\frac{x}{3}[/tex]- The solution is outlined below:
[tex]\begin{gathered} \frac{x-3}{2}-4<\frac{x}{3} \\ \\ Collect\text{ like terms:} \\ Add\text{ 4 to both sides and Subtract }\frac{x}{3}\text{ from both sides} \\ \\ \frac{x-3}{2}-\frac{x}{3}<4 \\ \\ We\text{ need the LCM of 2 and 3. } \\ The\text{ LCM is }2\times3=6 \\ \\ Thus,\text{ multiply both sides by 6 in order to remove the denominator} \\ 2\frac{}{} \end{gathered}[/tex][tex]\begin{gathered} 6\left(\frac{x-3}{2}\right?-6\left(\frac{x}{3}\right?<4\times6 \\ \\ 3\left(x-3\right)-2x<24 \\ Expand\text{ the bracket} \\ 3x-9-2x<24 \\ x-9<24 \\ Add\text{ 9 to both sides} \\ x<33 \end{gathered}[/tex]Final Answer
The answer is x < 33
{(7, 3), (4, 8), (-6, -5), (6, 6), (-1, 9) }
Domain:
Range:
Answer:
Domain: -6,-1,4,6,7
Range: -5,3,6,8,9
Step-by-step explanation:
The domain is the first element in each ordered pair. It is the x value. The range is the second element in each ordered pair. It is the y values.
A circle passes through (-2, 6) , (2, 8) , and (5, -1) Using the general form of a circle and the points above, fill in missing numbers to create the system of equations. (-2, 6) creates D + E + 1F = (2, 8) creates D + E + 1F = (5, -1) creates D + E + 1F = Solve the system of equations that you created, and write the equation for the circle by filling in the values for D, E, and F.
The equation of the circle passing through points (-2, 6) , (2, 8) , and (5, -1) is given as follows:
(x - 2)² + (y - 3)² = 25.
Equation of a circleThe equation of a circle with center (x*, y*) and radius r is given according to the following rule:
(x - x*)² + (y - y*)² = r².
The circle passes through point (-2,6), hence the first equation of the system is given as follows:
(-2 - x*) + (6 - y*)² = r².
r² = x*² + 4x* + 4 + y*² - 12y* + 36.
The circle also passes through point (2,8), hence the second equation of the system is given as follows:
(2 - x*) + (8 - y*)² = r².
r² = x*² - 4x* + 4 + y*² - 16y* + 64.
The final point is point (5,-1), meaning that the third equation is:
(5 - x*) + (-1 - y*)² = r².
r² = x*² - 10x* + 25 + y*² + 2y* + 1.
The system of equations to find the coordinates of the center and the radius is given as follows:
x*² + y*² + 4x* - 12y* + 40 - r² = 0.x*² + y*² - 4x* - 16y* + 68 - r² = 0.x*² + y*² - 10x* + 2y* + 26 - r² = 0.The solution to the system is given as follows:
x* = 2, y* = 3, r² = 25.
Hence the equation of the circle is:
(x - 2)² + (y - 3)² = 25.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,-8) and (1,4)
Answer: (8,
-4) and (3,8)
Step-by-step explanation:
