Answer: 506,150
First we must divided 0.9 into 530,000 to find out how much of the population will decrease each year.
0.9% of 530,000 is 4770. Which means that each year, 4,770 people will move the District of Columbia. From 2010 to 2015, that is 5 years, which means that we have to multiply 4,770 by 5.
4770 x 5 is 23850.
Next we have to subtract the amount of people who moved.
530,000- 23,850 is 506,150
This means by 2015, the expected population will be 506,150 in the District of Columbia.
I hope this helped & Good Luck <3 !!!
Frets are small metal bars positioned across the neck of a guitar so that the guitar can produce the notes of a specific scale. To find the distance a fret should be placed from the bridge, multiply the length of the string by 2−12, where n is the number of notes higher than the string’s root note. Where should a fret be placed to produce a G note on the E string (3 notes higher)
1)List what is given in this word problem?
2)state the equation for desmos 5
3)what is the X value? x = ?
4)what is the Y valuie? y = ?
Since the length of the string is not specified, we cannot find the Y value (fret position) exactly.
Given in this word problem:
Length of the string: Not specified
Number of notes higher than the root note: 3 (G note is 3 notes higher than the E string's root note)
Scale: Not specified
The equation for the fret position can be represented as follows:
fret position = length of string * 2^(-12 * n)
where n is the number of notes higher than the root note.
To find the X value, we need to know the length of the string, which is not specified in the problem.
To find the Y value, we need to calculate the fret position using the equation:
fret position = length of string * 2^(-12 * n)
fret position = length of string * 2^(-12 * 3)
fret position = length of string * 2^-36
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(2+5root7)/(2-5root7) = a+b root7
class 9
with complete explanation pls
The value of a and b are -179/171 and -20/171 respectively.
What is rationalization of surd?Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. In more complex cases, it is useful to multiply the denominator by its conjugate to cancel out the surds in the denominator.
(2+5√7)/(2-5√7)
by rationalization
(2+5√7)/(2-5√7) × (2+5√7)/(2+5√7)
=( 4+10√7 + 10√7 + 175)/4+10√7 - 10√7- 175
= (20√7+179)/-171
= -20/171 √7 -179/171
therefore the value of a = -179/171 and b = -20/171
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When graphed in the xy-plane, what is the y-coordinate of the vertex of the parabola with equation y=-3(x-4)(x+6)
Answer: A
Step-by-step explanation:
Convert the equation into quadratic form (y=ax^2+bx+c)
y=-3(x-4)(x+6) = y=-3x^2-6x+72
Calculate -b/2a
which is 6/-6=-1
then put the value -1 into the equation for x.
-3+6+72=75
The answer is therefore A.
a door of length 2m and breadth 1m is fitted in a wall. The length of the wall is 4.5m and the breadth is 3.6m. Find the cost of white washing the wall, if the rate of white washing the wall is rupees20 per metre square
Answer:
16.2m^2
16.2*20=324
324 rupees
Step-by-step explanation:
the cash price of a bike is 220. hire-purchase is 300 .if the deposit is 10% followed by 10 equal monthly installments find the amount you pay each month
Answer:
$27/month
Step-by-step explanation:
300-220=80
100%= 300
1%= 300÷100
= 3
10%= 3×10
= 30
300-30=270
270÷10= $27
Express the radical using the imaginary unit, i
Express your answer in simplified form.
Answer:
Step-by-step explanation:
root of -48 is equal to 4iroot3, so plus/neg 4iroot3
The number of observations will always be the same as the?A sample size. B. number of elements.C. number of variables. D. population size.
The number of observations will always be the same as the sample size. Therefore, the answer is A.
What is permutation ?
In mathematics and statistics, a permutation refers to a way of arranging a set of objects in a particular order. More specifically, a permutation is an arrangement of a set of distinct objects in a specific order. For example, if we have the set {1, 2, 3}, there are six possible permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}.
In permutations, the order of elements matters, which means that changing the order of any of the elements will result in a different permutation. Permutations are used in many areas of mathematics and statistics, including combinatorics, probability theory, and group theory. They are also used in computer science and cryptography for generating random sequences and encryption keys.
According to given conditions:
The number of observations refers to the number of data points or cases that you have in your dataset. For example, if you're collecting data on the heights of people in a certain population, each person's height measurement would be considered one observation.
A sample size, on the other hand, refers to the number of observations that you have included in your sample from the larger population. For example, if you're taking a random sample of 100 people from a population of 10,000, your sample size would be 100.
The number of elements typically refers to the number of individual items or units that you're measuring or counting. For example, if you're counting the number of cars in a parking lot, the number of elements would be the total number of cars.
The number of variables refers to the number of characteristics or attributes that you're measuring for each observation. For example, if you're collecting data on people's heights, weights, and ages, you would have three variables.
Finally, the population size refers to the total number of individuals or units in the population that you're interested in studying. This may or may not be relevant depending on the type of analysis you're doing. If you're conducting a sample survey, for example, the population size would be important to determine the appropriate sample size.
The number of observations will always be the same as the sample size. Therefore, the answer is A.
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Find the value of y.
Find the value of x.
Answer:
y=4,x= -1
Step-by-step explanation:
2y-3 =y+1
2y-y=1+3
y=4
∆CBD
2x+7=2y-3
2x+7=5
2x= 5-7
2x= -2
x= -1
What is the area of this figure? 3 m 3 m 9 m 9 m 6 m square meters 12 m
Answer: figure 1 is 9
figure 2 is 81
figure 3 is 72
= 162
Step-by-step explanation:
FLOWER GARDEN Erin is planning her summer garden. The table shows the number of bulbs she has according to type and color of flower. If Erin randomly selects one of the bulbs, what is the probability that she selects a bulb for a yellow flower or a dahlia? Round your answer to the nearest tenth of a percent.
Probability that Erin selects a bulb for a yellow flower or a dahlia is 52.8%.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Given, by the table
Total number of flowers = 5+4+3+3+1+2+2+5+6+0+1+4 = 36
Number of yellow flowers = 4 + 1 + 5 + 1 = 11
Number of Dahlia flowers = 5 + 4 + 3 = 12
Number of yellow Dahlia = 4
Probability of selecting bulb for a yellow flower P(y)= 11/36
Probability of selecting bulb for dahlia P(d) = 12/36
Probability of selecting bulb for yellow Dahlia P(y and d) = 4/36
Probability of selecting bulb for yellow flower or dahlia
= P(y) + P(d) - P(y and d)
= 11/36 + 12/36 - 4/36
= (11 + 12 - 4)/36
= 19/36
= 0.528
= 52.8%
Hence, 52.8% is probability that she selects a bulb for a yellow flower or a dahlia.
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A laundry detergent box measures 12 inches by 8 inches by 2.5 inches. What is the volume of the detergent box?
Answer:
240in^3
Step-by-step explanation:
V = whl
= (12in)(8in)(2.5in)
= 240 in ^3
The width of a rectangle is 4.25y-7.5 feet and its length is 7.5y+8 feet. Find the perimeter of the rectangle.
Answer:
23.50y+1
Step-by-step explanation:
2(4.25y-7.5+7.5y+8)
2(4.25y+7.5y-7.5+8)
2(11.75y+0.5)
2(11.75y) + 2(0.5)
23.50y + 1
prove 2^a , 2^b , 2^c forms a geometric sequence when a , b , c forms an arithmetic sequence.
Answer: Given that a, b, and c form an arithmetic sequence, so they are equally spaced, meaning the difference between each of them is constant. Let's denote the common difference between a, b, and c as d.
So, we have:
a = b - d
c = b + d
Using these two equations, we can prove that 2^a, 2^b, and 2^c form a geometric sequence.
We have:
2^a = 2^b / 2^d
2^c = 2^b * 2^d
Since the product of two powers of the same base is equivalent to the power of the base with the sum of the exponents, we have:
2^a * 2^c = 2^b * 2^b * 2^d * 2^d = 2^(b+b+d+d) = 2^(2b+2d)
So, we have:
2^a * 2^c = 2^(2b+2d) = 2^(2b) * 2^(2d) = 2^b * 2^b * 2^d * 2^d = 2^b * 2^c
This means that 2^a, 2^b, and 2^c form a geometric sequence, with the common ratio of 2^d.
Step-by-step explanation:
the process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles is:
The process of converting individual raw scores in a distribution to a set of scores for which we know the percentiles is known as "normalizing the data" or "standardizing the data."
The steps for standardizing the data are as follows:
Order the raw scores in the distribution from smallest to largest.
Assign each score a percentile rank. This is the percentage of scores in the distribution that are equal to or lower than the score. For example, if a score has a percentile rank of 75, it means that 75% of the scores in the distribution are equal to or lower than that score.
Convert the raw scores to standardized scores (also known as z-scores). This is done by subtracting the mean of the distribution from each score and then dividing by the standard deviation of the distribution. The resulting standardized score represents the number of standard deviations above or below the mean that the raw score falls.
The process of standardizing the data helps to put the raw scores into a common context, which makes it easier to compare scores from different distributions and to draw meaningful conclusions about the data. Additionally, standardized scores can be used to determine the probability of a score falling within a particular range.
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The area of a rhombus is 360 sq cm if one of its diagonal is 40 cm , find the other diagonal
Based on the information of area of rhombus and length of diagonal, the other diagonal of rhombus is 10.5 cm in length.
The diagonal and area of rhombus are related to each other by the formula -
Area = diagonal1 × diagonal2/2
Keep the values in formula to find the diagonal.
360 = 40 × diagonal 2/2
Rewriting the formula -
Diagonal 2 = (360 × 2)/40
Performing multiplication on Right Hand Side of the equation
Diagonal 2 = 420/40
Performing division on Right Hand Side of the equation
Diagonal 2 = 10.5 cm
The other diagonal is 10.5 cm.
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√52x^4 solve ……………….
Answer:
2[tex]\sqrt{13x^{2} }[/tex]
Step-by-step explanation:
To simplify the expression √52x^4, we can break it down as follows:
√(52x^4) = √(4 * 13 * x^4)
Since the square root of a product is equal to the product of the square roots, we can simplify further:
√(4 * 13 * x^4) = √4 * √13 * √(x^4)
The square root of 4 is 2, and the square root of x^4 is x^2:
2 * √13 * x^2
Therefore, the simplified expression is 2√13x^2.
Answer:
[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{52x^4}[/tex]
Prime factorization is the process of representing a positive integer as a product of its prime factors.
The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:
[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]
[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]2\sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]
[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]
[tex]2\sqrt{13} \;x^2[/tex]
Therefore, the simplified expression is:
[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]
Need help (Just started circles) please explain how to solve every thing.
Solve the system of linear equations by substitution.
y=4x
x+y=-10
By substituting the linear equations, we know that the value of x and y are -2 and -8 respectively.
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Ax+By=C is the usual form for two-variable linear equations.
A standard form linear equation is, for instance, 2x+3y=5.
When an equation is given in this format, finding both intercepts is rather simple (x and y).
So, we have the equation:
y=4x ...(1)
x+y=-10 ...(2)
Now, substitute y = 4x in equation (2):
x+y=-10
x+4x=-10
5x = -10
x = -10/5
x = -2
Then, substitute x = -2 in equation (1):
y = 4x
y = 4(-2)
y = -8
Therefore, by substituting the linear equations, we know that the value of x and y are -2 and -8 respectively.
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Write the ratio for cos a! Please
The ratio of the CosA will be 12 / 37 for the right-angle triangle.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that there is a right angle triangle having the Hypotenuse = 37, Base = 12, and Height = 35.
The value of CosA will be calculated as:-
CosA = Base / Hypotenuse
CosA = 12 / 37
Therefore, the ratio of the CosA will be 12 / 37 for the right-angle triangle.
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HELP ASAP WILL GIVE BRAIN DUE IN 20 MIN
Answer:
E
Step-by-step explanation:
I need help , come on ! Please
(a) The equation to find x is 4x + 22 = 90.
(b) The degree of each angle:
m∠1 = 51°m∠2 = 39°The sum of angle 1 and 2 is equal to right angle.
What is the value of right angle?The value of a right angle is equal to 90°.
In the figure, we have a right angle and one line in it. It makes two angles 1 and 2 with
m∠1 = (3x)°m∠2 = (x + 22)°(a) Find an equation to find x!
(b) Find the degree measure of each angle!
The sum of angle 1 and 2 is equal to 90°. So,
m∠1 + m∠2 = 90
3x + x + 22 = 90
4x + 22 = 90
This is the equation to find x. Then, we find x.
4x + 22 = 90
4x = 90 - 22
4x = 68
x = 68/4
x = 17°
The degree measure of each angle will be
m∠1 = 3x
m∠1 = 3(17)
m∠1 = 51°
m∠2 = x + 22
m∠2 = 17 + 22
m∠2 = 39°
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Find the number that is exactly halfway between 1/10 and 4/5
Answer:
Step-by-step explanation:
1/10 = 0.1
4/5 = 0.8
What's halfway between 1 and 8?
Let's show it on a number line:
¬ ¬
_0____1____2_____3______4_____5____6_____7_____8__________
It's 4 and 5, therefore it's 4.5
0.45 comes halfway through 1/10 and 4/5
Expressed as a fraction: 45/100 = 9/20
Hope that helps! Please make me brainliest!
Answer: 0.45
Step-by-step explanation:
Joey is training for a 5k race. She runs the same distance two days in a row. On the first day, she runs 5 laps around the track, and then runs additional 1. 5 miles. The next day she runs 3 laps, and an additional 4 miles. Analyze the text to answer the following questions
Answer:
Step-by-step explanation:
What is Joey's total distance run on the first day?
Joey runs 5 laps around the track, which we can assume is 1 mile per lap. So, she runs 5 miles. Additionally, she runs 1.5 miles, so her total distance run on the first day is 5 + 1.5 = 6.5 miles.
What is Joey's total distance run on the second day?
Joey runs 3 laps around the track, which we can assume is 1 mile per lap. So, she runs 3 miles. Additionally, she runs 4 miles, so her total distance run on the second day is 3 + 4 = 7 miles.
Lauren spent 1^3/8 hour cleaning the house, 7/8 hour doing the laundry, and 1^5/8 preparing food. How many hours did Lauren spend doing all the work?
Need step by step please.
Lauren spent a total of 10 hours on the duties if he spent 1 3/8 hour cleaning, 7/8 hour doing laundry, and 1 5/8 cooking dinner.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
Here,
To find the total time Lauren spent on the tasks, we need to add the time she spent cleaning the house, doing the laundry, and preparing food.
Cleaning the house: 1 3/8 hours
Doing the laundry: 7/8 hours
Preparing food: 1 5/8 hours
Adding these three quantities, we get:
1 3/8 + 7/8 + 1 5/8 = 1 3/8 + 7/8 + (2 3/8)
Next, we simplify each fraction by finding a common denominator of 8:
(18/8) + (7/8) + (28/8) = 1 + 7 + 2 = 10
So, Lauren spent a total of 10 hours on the tasks if he spent 1 3/8 hour cleaning the house, 7/8 hour doing the laundry, and 1 5/8 preparing food.
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Given rectangle C D E F below, DG = 15 If CG = 3x+6, solve for x
The numerical value of x in the expression 3x + 6 is 3.
What is the numerical value of x?The diagonals of a rectangle bisects each other and are equal.
Given that;
DG = 15CG = 3x + 6Value of x = ?Since the diagonals of a rectangle bisects each other and are equal.
DG = CG
Plug in the given values and simplify.
15 = 3x + 6
Solve for x
Subtract 6 from both sides
15 - 6 = 3x + 6 - 6
9 = 3x
Divide both sides by 3
9/3 = 3x/3
9/3 = x
3 = x
x = 3
Therefore, the value of x is 3.
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Which statements are true the ordered pair (1, 2) and the system of equations?
y=-2x+4
7z-2y=3
Select each correct answer.
O The ordered pair (1, 2) is not a solution to the system of linear equations.
When (1, 2) is substituted into the second equation, the equation is true.
Q. When (1, 2) is substituted into the first equation, the equation is false.
□ When (1, 2) is substituted into the second equation, the equation is false
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of inear equations.
Answer:
The statements that are true about the ordered pair (1, 2) and the system of equations are:
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.
So, the correct options are:
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.
Step-by-step explanation:
Given that f(x)= ax/bx-4, x≠4/b, x≠0. If f(1)=-2 and f(2)=2, find a+b.
The sum of a and b is obtained as follows:
a + b = 5.
How to obtain the values of a and b?The function for this problem is defined as follows:
f(x) = ax/[bx - 4]
f(1) = -2 means that when x = 1, y = -2, hence:
-2 = a/(b - 4)
a = -2b + 8
f(2) = 2 means that when x = 2, y = 2, hence:
2 = 2a/(2b - 4)
2a = 4b - 8
a = 2b - 4.
Equaling the two equations, the value of b is obtained as follows:
-2b + 8 = 2b - 4
4b = 12
b = 3.
Hence the value of a is ob:
a = 2b - 4
a = 2(3) - 4
a = 2.
Hence the sum is of:
a + b = 2 + 3
a + b = 5.
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an expression is given. -2y+3/2x+7/4 which are equivalent to the given expression select each answer
Option D and E are equivalent to the given expression.
How to find equivalent expressionFirst we find the x and y values of the equation -2y+3/2x+7/4.
For example x= 0, substitute:
-2y+3/2x+7/4=0
-2y=-7/4
y=7/8
For example y=0, substitute:
-2y+3/2x+7/4=0
3/2x=-7/4
x=-7/6
Then we look for choices A, B, C, D and E, which one produces x=-7/6 and y=7/8 if for example x=0 and y=0.
And those that have the same value are equations D and E.
What is equivalent equation?Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class, but also in everyday life.
The simplest example of an equivalent equation doesn't have any variables.
For example, these three equations are equivalent to each other:
3 + 2 = 5
4 + 1 = 5 5 + 0 = 5
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I need help solving this problem
The width of the rectangular will be x+4.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
Area of the rectangle is A = a*b
Given Length is = x+7
And the area is x² +11x+28
So the width is = x² +11x+28 / x+7
x² +7x+4x+28/x+7
=(x+7)(x+4)/x+7
=x+4
Hence the width of the rectangular will be x+4.
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pls I need solutions to this. find the sum of the 1st and three term of the gp, whose 3rd term is 27 and whose 6th term is 8
The sum of the 1st and three-term of the GP is 87.75.
What is geometric progression?
A geometric progression often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.
Here, we have
Given: 3rd term is 27 and whose 6th term is 8
Let the GP terms are a, ar, ar², ar³, ar⁴ and ar⁵,
Given ar² = 27 and ar⁵ = 8
Take the ratio of the sixth term to the third term:
ar⁵ / ar² = 8/27 => r³ = (2/3)³
r = 2/3
We know that
ar² = a(2/3)² = 27
=> a(4/9) = 27
=> a = 27*9/4 = 243/4
So, the terms are 243/4, 243/4*(2/3), 243/4*(4/9), 243/4*(8/27), 243/4*(16/81), 243/4*(32/243)
= 243/4 + 27
= 60.75 + 27
= 87.75
Hence, the sum of the 1st and three-term of the GP is 87.75.
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