Answers
Answer:
Of 20,000 people that apply, 6300 actually enroll.
Step-by-step explanation:
70% of 20,000 is 14,000
45% of 14,000 is 6,300
Related Questions
20 POINTSSS!!! Graph the ellipse.
Name the coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse.
Answers
The coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse. is (2,-1+3√3) & (2,-1 -3√3).
Calculation:-
[tex]\sqrt{1-\frac{a^{2} }{b^{2} } } =\sqrt{1-\frac{9}{36} } =\sqrt{\frac{36-9}{36} }[/tex]
= [tex]\sqrt{\frac{27}{36} } = \frac{\sqrt{3} }{2}[/tex]
=( b,H ± be) = (2, -1 ± 6x [tex]\frac{\sqrt{3} }{2}[/tex])
(2,-1+3√3) & (2,-1 -3√3).
The long axis is called the major axis and the short axis is called the minor axis. Each major axis endpoint is an ellipse vertex, and each minor axis endpoint is an ellipse vertex. The center of the ellipse is the center of both the major and minor axes. The endpoints of the principal axis are called vertices.
The midpoint of focus is the center of the ellipse. The minor axis is a line segment perpendicular to the major axis, passing through the center, and having ellipses at both ends. Ellipse focal points are two reference points that help draw the ellipse. The foci of the ellipse are on the major axis of the ellipse, equidistant from the origin. An ellipse represents the location of a point that is a constant distance from two fixed points.
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In a certain country, 9/50 of college freshmen major in chemistry. A community college in a region of the country has a freshman enrollment of approximately 900 students. How many of these freshmen might we project are majoring in chemistry
Answers
AS per the unitary method, the number of freshmen majoring in chemistry are 162.
Unitary method:
Unitary method defied as a process of finding the value of a single unit, and based on the known values.
Given,
In a certain country, 9/50 of college freshmen major in chemistry. A community college in a region of the country has a freshman enrollment of approximately 900 students.
Here we need to find the the number of freshmen majoring in chemistry.
As per the concept of unitary method, let us consider x be the number of freshmen majoring in chemistry.
So, we know that, 9/50 of college freshmen major in chemistry.
The total number of students in the community colleges is 900.
Therefore, the number of freshmen in it is calculated as
x = 900 x 9/50
x = 18 x 9
x = 162
Therefore, there are 162 freshmen in chemistry.
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A baker can bake 20 cupcakes in two hours, 30 cupcakes in three hours, and 40 cupcakes in four hours. What is the constant rate of change?
Answers
A baker can bake 20 cupcakes in two hours, 30 cupcakes in three hours, and 40 cupcakes in four hours.
so, the rate can be calculated as following:
number of cupcakes over the number of hours
So,
[tex]\begin{gathered} \frac{20}{2}=10 \\ or,\frac{30}{3}=10 \\ or,\frac{40}{4}=10 \end{gathered}[/tex]find the coordinates of the ends of each latus rectum and equations of asymptotes.
Answers
For conic section of the form:
[tex](\frac{x^2}{a^2})-(\frac{y^2}{b^2})=1[/tex]The Ends of the Lactus Rectum is given as:
[tex]L=(ae,\frac{b^2}{a}),L=(ae,\frac{-b^2}{a})[/tex]The e in the equation above is the Eccentricity of the Hyperbola.
This can be obtained by the formula:
[tex]e=\frac{\sqrt[]{a^2+b^2}}{a}[/tex]Thus, comparing the standard form of the conic with the given equation, we have:
[tex]\begin{gathered} \frac{(y+8)^2}{16}-\frac{(x-3)^2}{9}=1 \\ \text{This can be further expressed in the form:} \\ \frac{(y+8)^2}{4^2}-\frac{(x-3)^2}{3^2}=1 \\ By\text{ comparing this with:} \\ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \\ We\text{ can deduce that:} \\ a=4;b=3 \end{gathered}[/tex]Then, we need to obtain the value of the Eccentiricity, e.
[tex]\begin{gathered} e=\frac{\sqrt[]{a^2+b^2}}{a} \\ e=\frac{\sqrt[]{4^2+3^2}}{4} \\ e=\frac{\sqrt[]{16+9}}{4} \\ e=\frac{\sqrt[]{25}}{4}=\frac{5}{4} \end{gathered}[/tex]Hence, the coordinate of the ends of the each lactus rectum is:
[tex]\begin{gathered} L=(ae,\frac{b^2}{a}),L=(ae,\frac{-b^2}{a}_{}) \\ L=(4\times\frac{5}{4},\frac{3^2}{4}),L=(4\times\frac{5}{4},\frac{-3^2}{4}) \\ L=(5,\frac{9}{4}),L=(5,\frac{9}{4}) \end{gathered}[/tex]Please Help! Parallel Lines and Transversals!
Answers
Answer: No they are not parallel
The tallest tree in the United States
Coast Redwood in Jedidiah Smith State
Park in California. It is 321 feet tall.
Suppose you are 5 feet 8 inches tall and
cast a shadow that is 2 feet at a certain
time of day. About how long is the tree's
shadow at the same time of day? (convert
5 ft 8 inches to feet)
Answers
x = 113.2941 is the approximate length of the tree's shadow at the same time of a day.
What is a length?A unit of length is any arbitrarily chosen and widely accepted reference standard for measuring length. The most common units in modern use are metric units, which are used in every country on the planet. In the United States, customary units are also used. British Imperial units are still used in the United Kingdom and other countries for a variety of purposes. SI and non-SI units are subsets of the metric system.
5 feet + 8 inches is equal to 5 feet.
5 feet 8 inches is equal to 5 feet plus (8 inches) * (1 foot 12 inches).
5 feet 8 inches plus (8/12) feet equals 6 feet.
5 feet 8 inches equals 5 feet plus 2/3 feet.
5 feet 8 inches = (5 + (2/3)) feet
5 feet 8 inches = ((15/3) + (2/3)) feet
5 feet 8 inches = ((15+2)/3) feet
5 feet 8 inches = (17/3) feet
5 feet 8 inches = 5.667 feet
A/B = C/D
where
A = height of person
B = length of shadow of person
C = height of tree
D = length of shadow of tree
So we have
A = 17/3
B = 2
C = 321
D = x
A/B = C/D
(17/3)/2 = 321/x
(17/3)*x = 2*321
(17/3)*x = 642
(3/17)*(17/3)*x = (3/17)*642
x = 1926/17 the precise length of the tree's shadow
The approximate length of the tree's shadow is x = 113.2941.
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Which number is IRRATIONAL?A)V12B)136C)V64D)V144
Answers
An irrational number is a number that cannot be written as a fraction - the decimal goes on forever without repeating. Therefore:
[tex]\sqrt[]{12}=2\sqrt[]{3}=3.46410[/tex]in this case it cannot be expressed as a fraction and it is decimal, this is the correct option. So,
answer A.
>)How many people were surveyed about their favorite pets?A) 46B) 34C36D) 44
Answers
ANswer:
From the bar diagram,
Number of people own rabbit as pet = 4
Number of people own dog as pet = 8
Number of people own cat as pet = 11
Number of people own goldfish as pet = 6
Number of people own hamster as pet = 5
So, the number of people surveyed about their favorite pets equals the sum of number of people own rabbit, dog, cat, goldfish or hamster as pet.
Number of people surveyed about their favorite pets
[tex]\begin{gathered} =4+8+11+6+5 \\ =34 \end{gathered}[/tex]Hence 34 people surveyed about their favorite pets.
Option B is correct.
Six more than three times a number is negative thirty-six.
Answers
x = 10 is the value of x as per given in the question.
What is linear equation ?A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables and A and B are: Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line. A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. There is a linear equation in one variable and a linear equation in two variables.Calculation3x + 6 = 36
3x = 30
x = 10
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What is the equation of this line line PLS help
Answers
Answer: y=2x
Step-by-step explanation:
The equation of the line is y=2x.
what is 60 rounded to the nearest whole number
Answers
Answer: I suppose it is still 60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
becaus eit the whole nimber
Given 3 and one-tenth times negative 6 times seven-twelfths, determine the product.
eighteen and one sixtieth
negative eighteen and 7 over 120
ten and 17 over 20
negative 10 and 17 over 20
Question 2(Multiple Choice Worth 2 points)
(One-Step Inequalities MC)
Write the statement "the sum of a number and 18.4 is at least −3.8" as an inequality.
−3.8 + b > 18.4
b + 18.4 ≥ −3.8
b + 18.4 ≤ −3.8
−3.8 + b < 18.4
Question 3(Multiple Choice Worth 2 points)
(Adding and Subtracting Rational Numbers MC)
Simplify negative 3 and two-thirds minus 6 and three-fourths.
3 and one-half
negative 10 and one-twelfth
negative 10 and five-twelfths
negative 18 and one-half
Question 4(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
Question 5(Multiple Choice Worth 2 points)
(Dividing Rational Numbers MC)
Divide negative 3 and one-sixth ÷ negative 8 and two-fifths.
252 over 95
95 over 252
51 over 30
30 over 51
Question 6(Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve one eighth times quantity x plus 32 end quantity equals negative 7.
x = 56
x = 7
x = −88
x = −24
Question 7(Multiple Choice Worth 2 points)
(Rewriting Rational Numbers LC)
Which number is equal to four and one-sixth?
four and sixteen hundredths with the six repeating
six twenty-fifths
4.2
416%
Question 8(Multiple Choice Worth 2 points)
(Laws of Exponents with Whole Number Exponents LC)
Which expression is equivalent to 2 and one tenth raised to the fifth power divided by nine tenths raised to the fourth power, all raised to the fifth power?
0.55
0.56
2 and one tenth raised to the twenty fifth power divided by nine tenths raised to the twentieth power
2 and one tenth raised to the tenth power divided by nine tenths raised to the ninth power
Question 9(Multiple Choice Worth 2 points)
(Adding and Subtracting Rational Numbers MC)
Julie wanted to match Lisa's obstacle course record of 68.2 seconds. She has already spent thirty-nine and one fourth seconds on wall climbing and 12.84 seconds on the ropes. How much time did she have left to match the record?
12.24 seconds
16.11 seconds
26.41 seconds
28.95 seconds
Question 10(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Write the math sentence as an equation: Negative nine times the sum of a number and 12.3 is 30.8
−9(r − 12.3) = 30.8
−9r + 12.3 = 30.8
−9r − 12.3 = 30.8
−9(r + 12.3) = 30.8
Question 11(Multiple Choice Worth 2 points)
(Laws of Exponents with Whole Number Exponents MC)
Evaluate two and two tenths raised to the sixth power divided by two and two tenths raised to the fifth power, all raised to the second power.
4.84
4.4
2.2
1
Question 12(Multiple Choice Worth 2 points)
(Adding and Subtracting Linear Expressions MC)
Write the expression in simplest form.
the quantity negative three fifths x minus 8 end quantity minus the quantity negative 14 plus three tenths x end quantity
negative nine tenths x plus 6
negative nine tenths x minus 6
negative three tenths x minus 6
negative three tenths x plus 6
Question 13(Multiple Choice Worth 2 points)
(Order of Operations MC)
Simplify the expression.
negative 15 plus the quantity negative 1 and six tenths plus 9 and 34 hundredths end quantity divided by 6 all times 3 squared minus 5 and 7 tenths
−4.125
−9.09
−12.96
129.09
Question 14(Multiple Choice Worth 2 points)
(Equivalent Linear Expressions LC)
Which expression is equivalent to −4(b − 5)?
−4b − 20
4b + 5
−4b + 20
−4b − 5
Question 15(Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve the equation for x.
−0.24x − 16.4 = 1.96
x = −60.2
x = 60.2
x = −76.5
x = 76.5
Answers
To solve the multiple questions performed, a process is being followed to get accurate results which are mentioned after the respective questions.
What are different operations in mathematics?Addition is the process of joining two or more numbers to determine their total. The result of adding the numbers 3 and 4 is 3 + 4 = 7, for instance. Any sort of number, including whole integers, fractions, decimals, and even negative values, can be added to.
The process of subtracting involves calculating the difference between two numbers. For example, subtracting 4 from 7 yields 7 - 4 = 3. Any sort of number, including whole integers, fractions, decimals, and negative values, can be subtracted.
Multiplication is the process of combining two or more numbers to determine their product. The result of multiplying the numbers 3 and 4 is 3 * 4 = 12, for instance. such as addition. Any kind of number may be used for addition, subtraction, and multiplication.
The act of dividing two integers involves determining their quotient. For example, dividing 12 by 4 yields 12 / 4 = 3. Any sort of value could be divided, although some combinations of numbers, such dividing by zero, are not described as division.
How to solve?
1) 3 * (-6) * (7/12) which is -7.5. So, the answer is -18 and 7/120 or negative 18 and 7 over 120.
2) -3.8 + b - 18.4 ≥ 0
-22.2 + b >= 0
∵sum of a number and 18.4 is at least -3.8, we can say that b is greater than or equal to -22.2.
∴b + 18.4 ≥ −3.8.
3) (-3/3) - (6/4) = (-9/3) - (6/4)
(-9/3) - (6/4) = (-9/3) * (4/4) - (6/4) * (3/3)
= (-36/12) - (18/12)
(-36/12) - (18/12) = -54/12 = -9/2 = -4 and 1/2
The correct answer is negative 18 and one-half.
4) 37.50w = $300
w = 8
37.5w + 155.95 = 455.95; w = 8.
5) (-7/6) / (-17/5) = (-7/6) * (5/17)
= (-35/102)
(-35/102) / (35/35) = (-1/3) / 1
= -1/3
6)x/8 + 32 = -7
x/8 = -39
x = -8 * -39
x = 8 * 39
x = 312
7)x = 56
x = 7
x = −88
x = −24
8)= [(2 and one tenth)^5] / [(9 tenths)^4]^5
= [2^5 * (1/10)^5] / [9^4 * (1/10)^4]^5
= [2^5 * (1/10)^5] / [9^4 * (1/10)^4]^5
= 2^5 * (1/10)^5 / (9^4 * (1/10)^4)^5
= 2^5 * (1/10)^5 / 9^4 * (1/10)^4 * 5
= 2^5 * (1/10)^5 / 9^4 * (1/10)^4 * 5
= 2^5 / 10^5 / 9^4 / 10^4 * 5
= 2^5 / (10^5 * 9^4) / 10^4 * 5
= 2^5 / (10^5 * 9^4) / 10^4 * 5
= 32 / (10^9 * 6561) * 5
= 32 / (10^9 * 6561) * 5
= 32 / 65610000 * 5
= 32 / 65610000 * 5
= 32 / 3285050000
= 32 / 3285050000
= 0.0000977077
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List the transformations.
Answers
The transformation of the equation [y = 4 - 1/2 √x + 3] is shown on the graph where the curve touched the x-axis on (61, 0).
What is a graph?To develop a graph is to make a diagram that depicts the relationship between two or more objects.
Make a sequence of bars on graph paper as an example of a graph.
Bar graphs, circle graphs, and line graphs are the three most often used types of graphs.
Different types of data can be displayed using different types of graphs.
So, plotting the equation on the graph as follows:
The equation: y = 4 - 1/2 √x + 3
Plot the equation on the graph:
(Refer to the graph attached below)
The curve touches the x-axis on the coordinate (61, 0).
Therefore, the transformation of the equation [y = 4 - 1/2 √x + 3] is shown on the graph where the curve touched the x-axis on (61, 0).
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Got It? Do this problem to find out.c. The number of games won in the American Football Conferencein a recent year is displayed below. Find the median and themeasures of variability. Then describe the data.American Football Conference Wins+10 11 12 131 2 3456 7 8 9
Answers
Answer:
Explanation:
The median is the value corresponding to the line inside the box. Looking at the box plot, the line is between 8 and 9. Thus,
Median = 8.5
To find the measure of variability, we would find the interquartile range, IQR
IQR = third quartile(Q3) - first quartile(Q1)
The first quartile is the value corresponding to the left end of the box. From the box plot, it is between 5 and 6. Thus,
Q1 = 5.5
The third quartile is the value corresponding to the right end of the box. From the box plot,
Q3 = 11
Thus,
IQR = 11 - 5.5
IQR = 5.5
The range is the difference between the minimum and maximum values. On the box plot,
maximum value = 13
minimum value = 1
Range = 13 - 1
Range = 12
Hello! Need a little help on this functions question. Thanks!
Answers
..
SOLUTION
EXPLANATION;
The range of the graph is:
[tex][-1,\infty)[/tex][tex]The\text{ range of f\lparen x\rparen=}\sqrt[\placeholder{⬚}]{x+1}-3\text{ is \lbrack-3,}\infty)[/tex]Therefore the difference is;
[tex][-3,-1)[/tex]pls help I was taught this concept today and I can't understand or get it right!! Find the measure of the arc or angle indicatedFind the measure of mPSQa) 53°b) 248°c) 72°d) 65°
Answers
Step 1:
Find the value of x
Using secant theorem
[tex]<\text{PQR =}\frac{1}{2}\text{ }\timesStep 2:If x = 9
Then 6x+2 = 6(9) + 2 = 54+2 = 56 degrees
The measure of arc PQ = 14(9) - 14 = 126 - 14 = 112 degrees
Step 3:
The total angle in a circumference is 360 degrees
Therefore ,
mPQ + mPSQ = 360
mPSQ = 360 - mPQ
mPSQ= 360 - 112 = 248degrees
The answer is option B
Kyle can was the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
Answers
No, they can not wash the car in less than 16 minutes while working together.
Given, Kyle can wash the car in 30 minutes.
Michael can wash the car in 40 minutes.
Now, we are asked that working together, can they wash the car in less than 16 minutes.
So, Kyle wash the car = 30 min
Kyle can wash (1/30)th part of the car in 1 min.
Michael wash the car = 40 min
Michael can wash (1/40)th part of the car in 1 min.
Kyle and Michael can together wash the ( 1/30 + 1/40 )th part of the car in 1 min.
Kyle and Michael = 1/30 + 1/40
Kyle and Michael = (4 + 3)/120
Kyle and Michael = 7/120
So, Kyle and Michael can together wash the 7/120th part of the car in 1 min.
and both can together wash the car in 120/7 min i.e. 17.14 min
So, working together both can wash the car in 17.14 min.
Hence, No, they can not wash the car in less than 16 minutes while working together.
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Please help now asap !!!
Answers
answer:
6378/2
step-by-step explanation:
dividing the largest number by the smallest number will allow for the greatest quotient. hope that helps!
Write the slope-intercept form for an equation of a line that is perpendicular to the graph of y=6x - 6 and passes through the x-intercept of that line.
Answers
Answer:
Step-by-step explanation:
ur mom
what are like terms
63 + 54
Answers
Answer:
There are 3 common factors of 63 and 54, that are 1, 3, and 9. Therefore, the greatest common factor of 63 and 54 is 9.
Step-by-step explanation:
In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match.
Hope this helped:)
if a/ b+1 = 2, what does 2b equal?
Answers
The Arnold Inn offers two plans for wedding parties. Under plan A, the inn charges $30 for each person in attendance. Under plan B, the inn charges $1300 plus $20 for each person in excess of the first 25 who attend. For what size parties will plan B cost less? I do not understand how for Plan b: 1300+20(p-25). I do not understand the part p-25
Answers
ANSWER
81 people
EXPLANATION
Let p be the number of people that attend the party.
Under plan A, the inn charges $30 for each person, so the value y of a party for p people is,
[tex]y_A=30x[/tex]Then, under plan B, the cost is $1300 for a maximum of 25 people - this means that if 1 to 25 people attend the party, the cost is the same, $1300. For each person in excess of the first 25 - this means for 26, 27, 28, etc, the inn charges $20 each. The cost for plan B is,
[tex]y_B=1300+20(p-25)[/tex]The last part, (p - 25), is the part of the equation that separates the first 25 attendees. This equation works for 25 people or more, but it is okay to solve this problem. Note that for p = 25, the cost for plan A is,
[tex]y_A=30\cdot25=750[/tex]Which is less than the cost of plan B ($1300).
We have to find for what number of people attending the party, the cost of plan B is less than the cost of plan A,
[tex]y_BThis is,[tex]1300+20(p-25)<30p[/tex]We have to solve this for p. First, apply the distributive property of multiplication over addition/subtract4ion to the 20,
[tex]\begin{gathered} 1300+20p-20\cdot25<30p \\ 1300+20p-500<30p \end{gathered}[/tex]Add like terms,
[tex]\begin{gathered} (1300-500)+20p<30p \\ 800+20p<30p \end{gathered}[/tex]Now, subtract 20p from both sides,
[tex]\begin{gathered} 800+20p-20p<30p-20p \\ 800<10p \end{gathered}[/tex]And divide both sides by 10,
[tex]\begin{gathered} \frac{800}{10}<\frac{10p}{10} \\ 80For 80 people, the costs of the plans are,
[tex]\begin{gathered} y_A=30\cdot80=2400 \\ y_B=1300+20(80-25)=1300+20\cdot55=1300+1100=2400 \end{gathered}[/tex]Both have the same cost. The solution to the inequation was the number of people, p, is more than 80. This means that for 81 people the cost of plan B should be less than the cost of plan A,
[tex]\begin{gathered} y_A=30\cdot81=2430 \\ y_B=1300+20(81-25)=2420 \end{gathered}[/tex]For 81 people, plan B costs $10 less than plan A.
4x^4 - 3x^3 + 2x^2 - 5x +6 divided by (x-2)what is the remainder of this question
Answers
The remainder is 44
Explanations:The given polynomial is:
[tex]4x^4-3x^3+2x^2-5x\text{ + 6}[/tex]The function is to be divided by x - 2
The remainder of the division will be calculated using the remainder theorem
The remainder theorem states that " If a function g(x) is divided by x - a, the remainder of the division will be g(a)"
[tex]\text{Let g(x) = 4x}^4-3x^3+2x^2-5x+6[/tex]The remainder when g(x) is divided by x -2 is g(2)
[tex]\begin{gathered} g(2)=4(2)^4-3(2)^3+2(2)^2-\text{ 5(2) + 6} \\ g(2)\text{ = 4(16) - 3(8) + 2(4) -5(2) + 6} \\ g(2)\text{ = 64 - 24 + 8 - 10 + 6} \\ g(2)\text{ = 44} \end{gathered}[/tex]pls help me wi this question
Answers
Answer:
1 block west and 8 blocks north
Step-by-step explanation:
One block east and two blocks north to the coffee shop. Subtract two blocks west from the one block east, and you get one block west. Add the six blocks north to the two blocks north, and you get eight blocks north.
The opposite of a number and sometimes negative true or false?
Answers
The given statement "Negative is the opposite of an integer" is FALSE.
What is an integer?A number that may be expressed without a fractional component is called an integer. For instance, while 9.75, 5+1/2, and 2 are not numbers, 21 and 4 and 2048 are.So, on the number line, opposite values are those that are equally spaced apart from zero.
Nevertheless, the values' signs will differ.Since both negative and positive numbers can be found in an integer. As a result, an integer's opposite is not always a negative. Take the numbers 3 and 8 as an example.These numbers' opposites are:
3 is the reciprocal of -3.8's polar opposite is -8.Therefore, the given statement "Negative is the opposite of an integer" is FALSE.
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Evaluate
107% of 700m
Answers
Answer:
834.6m
Step-by-step explanation:
780*1.07=834.6
Find 8th term for 10,-20,40
Answers
Answer:
-1280
Step-by-step explanation:
So, as we can see just by loooing at this geometric sequence, the factor is -2. Let's double check this.
10 * -2 = -20 * -2 = 40
We can just keep multiplying to find the 8th term!
40 * -2 = -80 * -2 = 160 *-2 = -320 * -2 = 640 * -2 = -1280
Sometimes with a short sequence, it is better to just multiply it out. You could also do it like this, though:
[tex]a_{n}=a_{1} *r^{n-1}[/tex]
Here, r = -2. We are looking for the 8th term, which would be 8
Plug in our values:
[tex]a_{8}=10*-2^{7}[/tex]
[tex]-2^{7}=-128\\[/tex]
[tex]10*-128=-1280[/tex]
That is the same answer we got before. I would suggest doing it mathematically if you have a long sequence (15, 100, 300 terms)
Hope this helped!
Find the equation of line containing given points. Write the equation in slope- intercept form (0,2)(2,-3)
Answers
Answer:
[tex]y=\frac{-5x}{2}\text{ + 2}[/tex]Explanation:
Here, we want to get the equation of the line
The general equation of a line in slope-intercept form is:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
We can get the equation through the following:
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) is (0,2) and (x2,y2) is (2,-3)
Substituting the values, we have it that:
[tex]\begin{gathered} \frac{y-2}{x-0}\text{ = }\frac{-3-2}{2-0} \\ \\ \frac{y-2}{x}\text{ = }\frac{-5}{2} \\ \\ \left(y-2\right)\text{ = }\frac{-5x}{2} \\ \\ y\text{ = }\frac{-5x}{2}\text{ + 2} \end{gathered}[/tex]GCF for 4y + xy2 + 6y
Answers
The greatest common factor or GCF in the expression 4y + xy² + 6y is y.
The given expression is 4y + xy2 + 6y
GCF stands for greatest common factor
Among these three numbers ;
the variable y is common in all three of them
The factors of 4 y = 4 and y
the factors of xy² are x and y
and the factors of 6y are 6 and y
This can also be simply written by taking y common in this
for example; y ( 4 + xy + 6 )
From the above mentioned proof we can establish the fact that the variable y is common in all three of them
Thus the greatest common factor among them is y
To know more about greatest common factor or related problems you may visit the link which is mentioned below;
https://brainly.com/question/11221202
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The population of a mosquito population obeys the law of uninhibited growth.If there are 500 mosquito initially and there are 800 after 1 day. How long is it until there are 7000 mosquito?Round your answer to the nearest tenth.
Answers
The law of uninhibited growth is express as:
[tex]N(t)=N_0e^{kt}[/tex]where N(t) is the population at time t, N0 is the initial population, k is the growth rate and t is the time. In this case we know that after one day, t=1, the population is 800 and that the initial population was 500; plugging these values and solving for k we have:
[tex]\begin{gathered} 800=500e^k \\ e^k=\frac{800}{500} \\ \ln e^k=\ln\frac{8}{5} \\ k=\ln\frac{8}{5} \end{gathered}[/tex]Now that we have the growth rate, we know that the population growth in this case can be express as:
[tex]N(t)=500e^{(\ln\frac{8}{5})t}[/tex]We want to know the time it takes for the population to be 7000, to find it we equate our expression to this value and solve for t:
[tex]\begin{gathered} 7000=500e^{(\ln\frac{8}{5})t} \\ e^{(\ln\frac{8}{5})t}=\frac{7000}{500} \\ \ln e^{(\ln\frac{8}{5})t}=\ln14 \\ (\ln\frac{8}{5})t=\ln14 \\ t=\frac{\ln14}{\ln\frac{8}{5}} \\ t=5.6 \end{gathered}[/tex]Therefore, it takes 5.6 days for the population to reach 7000 individuals.