The population at the onset as 250,000. There has been a 3.5% decrease every year.
The exponential decay function therefore is;
[tex]\begin{gathered} y=a(1-r)^t \\ a=250000,r=0.035,t=\text{time in years} \end{gathered}[/tex]Hence, to approximate what the population would be 7 years from now;
[tex]\begin{gathered} y=a(1-r)^t \\ y=250000(1-0.035)^7 \\ y=250000(0.965)^7 \\ y=250000\times0.779275\ldots \\ y=194818.9516 \\ y\approx194819\text{ (to the nearest whole number)} \end{gathered}[/tex]The population after 7 years shall be 194,819 people (rounded to the nearest whole number).
Please help
State if the three numbers can be the measures of the sides of a triangle. 1) 9, 7, 13 2) 26, 12, 11 3) 11, 2,9 4) 6, 11, 12 Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 5) 12,9 7) 11,6 6) 8, 11 8) 12,8
To determine if the three numbers can be the measures of the sides of a triangle:
According to the Triangle Inequality theorem to construct a triangle, the sum of the two sides of the triangle is greater than the third side i.e x + y>z
1) 9, 7, 13
So, 9+7 > 13
16 > 13
7+ 13 > 9
20 > 9
9+13 > 7
22 > 7
Yes, they can be the measures of the sides of a triangle.
2) 26, 12, 11
So, 26+12 > 11
38 > 11
12+ 11 > 26
23 < 26
No, they cannot be the measures of the sides of a triangle.
3) 11, 2,9
So, 11+2 > 9
13 > 9
2+ 9 > 11
11 = 11
No, they cannot be the measures of the sides of a triangle.
4) 6, 11, 12
So, 11+6 > 12
17 > 9
11+12 > 6 and 12+6 > 11
Yes, they can be the measures of the sides of a triangle.
To determine the range of the third side we find the maximum value and minimum value using two sides of a triangle.
Let's assume that x is the third side of the triangle.
5) 12,9
So, the maximum value of the third side is 12+9 = 21 and the minimum value is 12-9 = 3.
Hence, the range is 3<x<21.
6) 8, 11
The maximum value of the third side is 8+11 = 19 and the minimum value is 11-8 = 7.
Hence, the range is 3<x<19.
7) 11,6
The maximum value of the third side is 11+6 = 17 and the minimum value is 11-6 = 5.
Hence, the range is 5<x<17.
8) 12,8
The maximum value of the third side is 12+8 = 20 and the minimum value is 12-8 = 4.
Hence, the range is 4<x<20.
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Divide:
945) 8,880
R
Answer:
about 9.4
Step-by-step explanation:
Please help me on this question I need full explanation
Answer: parrallelograms have 4 sides
Step-by-step explanation:
One angle measures 170°, and another angle measures (6k + 44)°. If the angles are vertical angles, determine the value of k.
Answer:
21 = k
Step-by-step explanation:
Vertical angles are equal
170 = 6k+44
Subtract 44 from each side
170-44 = 6k+44-44
126 = 6k
Divide each side by 6
126/6 = 6k/6
21 = k
the equation y=12.7x+15.2 estimates the amount that businesses will spend, in billions of dollars, on internet software to conduct transactions via the web, where x is the number of years after 2002. for what years will the spending be more than $66 billion?
The years when the spending be more than $66 billion is in 4 years time.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The equation is given as y=12.7x+15.2 and the amount is $66 billion. Therefore, the value of x will be:
y=12.7x+15.2
66 = 12.7x + 15.2
Collect like terms
12.7x = 66 - 15.2
12.7x = 50.8
Divide
x = 50.8 / 12.7
x = 4
The number of years is 4.
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What is the terms of 2x+9+7x
The result of the expression 2x+9+7x is 9x+9
The expression is 2x+9+7x
To solve this expression, first we have to rearrange the terms and do the arithmetic operations in the expression.
Expressions is the mathematical statements that have a minimum of two terms containing numbers or variables, connected by an operator in between. The operator maybe addition, subtraction, division or multiplication. To solve the mathematical expression we have to do the arithmetic operation on like terms.
The expression is 2x+9+7x
Rearrange the terms in the expression
= 2x+7x+9
Add the like terms in the expression
= (2+7)x+9
= 9x+9
Hence, the result of the expression 2x+9+7x is 9x+9
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what is the probability of rolling at least one even number or a sum of 3 using two number cubes?
Answer:you could do
You would need to rile a two and a one together though
please help if you can
jeffrey has $1.20 more than ryan. when ryan hands jeffrey $7.50, jeffrey's money becomes 7 times as much as Ryan's. How much money did they each have at the beginning?
Answer:
Ryan had 10.20 dollars and Jeffery had 11.40 dollars.
Step-by-step explanation:
Let Ryan have x dollars originally, then Jeffrey has x + 1.20 dollars.
From the given info:
After getting 7.50 from Ryan, Jeffrey has:
x + 1.2 + 7.5 dollars and Ryan has x - 7.50 dollars.
Jeffreys money is now is 7 times as much as Ryan's, so:
x + 8.7 = 7(x - 7.5)
x + 8.7 = 7x - 52.5
8.7 + 52.5 = 7x - x
6x = 61.2
x = 10.20 dollars.
find the equation of ab and bc in the following square
In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
The formula for a2 + b2 + c2 is written as a square plus b square plus c square. A2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca) is how it is expanded.
Give an example to explain what square is?
A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. Many objects can be found in your surroundings that have a square shape.
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Arrange the terms of the polynomial in descending Then, determine the degree of
the polynomial, and name the polynomial by the number of terms.
5x 17X² + 22x
The terms of the polynomial, which has a degree of 2, are ordered as follows in decreasing order: 17x² + 27x
What in mathematics is a polynomial?Sums of terms of the form k⋅xⁿ where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5.
How should a polynomial be organized?Typically, polynomials are set up in one of two ways. Basically, ascending order is when a term's strength grows with each consecutive term. In essence, descending order occurs when a term's power declines with each consecutive term.Given polynomial: 5x + 17x² + 22x
We need to simplify this polynomial first.
5x + 17x² + 22x = 27x + 17x²
Now we will put the term with highest degree first and arrange the terms of this polynomial.
17x² + 27x
Since, the highest power of terms in this polynomial is 2.
We can say that the degree of polynomial is 2.
Therefore, the polynomial has a degree of 2 and its terms are arranged in decreasing order as follows: 17x² + 27x.
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A calculator displays 3.687E
–
6. How do you write 3.687E
–
6 in standard form?
The expression of the calculator form 3.687E in standard form is; 3.687 × 10¹
How to display a number in standard form?
A standard form of a number in Math's is simply the representation of large numbers or small numbers using exponents to represent such numbers in standard form.
The correct definition of standard form can be explained in terms of decimal numbers that follows particular rules. We know that decimal numbers are the simplified form of fractions.
Thus, any number that can be written in form of a decimal number, between 1 and 10, multiplied by a power of 10, is said to be in standard form.
Thus, 3.687E simply means;
3.687 × 10¹
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2/3x+2y=12 in standard form
Answer:
[tex]2x + 6y = 36[/tex]
[tex]x + 3y = 18[/tex]
PLS HELP 70 POINTS PLSSS!!!!!!!!!!!!!! ITS EASY
Circle A has a diameter of 9 cm. Circle B has a radius of 6 cm.
a.) Which circle has the larger circumference? A or B?
b.) About how many centimeters larger is it?
cm larger
(NO PICTURE INCLUDED) (DONT ASK FOR PIC)
Answer: B
Step-by-step explanation: B is larger by about 9.42 in
Rational Expressions
a) The area of a rectangle is x - (16/x). The width is (x/4) + 1. Find an expression to represent the length
b) The volume of a rectangular prism is (7/x) - (3/5x). The width is 2/x and the hight is 4/x, what is the length?
(a) The expression to represent the length of the rectangle is
h = (x-16/x)/(x/4+1).
(b) The length of the rectangular prism is L = ((7/x)-(3/5x))/(2/x)(4/x).
What is a rectangle?A rectangle is a quadrilateral with all four interior angles measures of 90°.
(a) Given that, the area of the rectangle is x-16/x and its width is x/4 +1.
Let the length of the rectangle be h, then it follows:
h×(x/4 + 1) = x - 16/x
h = (x-16/x)/(x/4+1)
Hence, the expression to represent the length of the rectangle is
h = (x-16/x)/(x/4+1).
(b) Given that, the volume of the rectangular prism is (7/x)-(3/5x), the width is 2/x, and the height is 4/x.
Let the length of the rectangular prism be L, then it follows:
L× (2/x) ×(4/x) = (7/x)-(3/5x)
L = ((7/x)-(3/5x))/(2/x)(4/x)
Hence, the length of the rectangular prism is L = ((7/x)-(3/5x))/(2/x)(4/x).
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For a walk-a-thon, a sponsor is committed to giving you a flat fee of $25 plus $7 for every mile (m) you walk. SOMEONE HELP ME!!!!!!!!!!!!
Answer:
how many miles did they walk
Step-by-step explanation:
you didn't put the full question
An angle measures 32.6° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
See below
Step-by-step explanation:
Supplementary angles sum to 180 degrees
x = angle 1
(x+32.6 ) = angle two
x + (x+32.6) =180
2x = 180-32.6
x = 73.7 angle 2 = 106.3°
Can someone solve this and explain the process
Sin 73° has a value of 0.9563. (approximately).
Define trigonometric ratios.Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle. If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.
Given Data
Trigonometric ratio of
sin73°
The sine trigonometric function for an angle of 73 degrees has a value of sin 73 degrees.
Sin 73° has a value of 0.9563. (approximately).
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the million americans of age and over control percent of all discretionary income. aarp estimated that the average annual expenditure on restaurants and carryout food was for individuals in this age group. suppose this estimate is based on a sample of persons and that the sample standard deviation is . round your answers to the nearest whole numbers. a. at confidence, what is the margin of error? b. what is the confidence interval for the population mean amount spent on restaurants and carryout food? , c. what is your estimate of the total amount spent by americans of age and over on restaurants and carryout food?
Using the t-distribution, it is found that:
a. The margin of error is of $122.4.
b. The 95% confidence interval for the population mean amount spent on restaurants and carryout food is of ($1,750.6, $1,995.4).
c. The estimate is the sample mean of $1,873.
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean, which is also the estimate of the population mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In the context of this problem, the values of these parameters are given by:
[tex]\overline{x} = 1873, s = 550, n = 80[/tex]
Hence, for item c, the estimate is of $1,873, as it is the sample mean.
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 80 - 1 = 79 df, is t = 1.9905.
The margin of error is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
Hence:
[tex]M = 1.9905\frac{550}{\sqrt{80}} = 122.4[/tex]
The confidence interval is the sample mean plus/minus the margin of error, hence:
1873 - 122.4 = $1,750.6.1873 + 122.4 = $1,995.4.What is the missing information?The problem is given by the image at the end of the answer.
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Which equation can be simplified to find the inverse of y = 5x² + 10?
Answer:
y=mx+b its decribe that
In triangle ABC, the measure of b is three times larger than the measure of C. The measure of A is twice as large as the measure of C. The sum of the angles in a triangle is 180°.
The value of angle a, b and c in the triangle are 60, 90 and 30 degrees respectively and the summation of these angles is equal to 180 degree.
Sum of Angles in TriangleThe total sum of angles in a triangle is equal to 180 degrees.
To solve this problem, we have to write out equations to represent the unknown values.
Let;
a = xb = yc = zMathematically,
[tex]a + b + c = 180^0[/tex]
Let's represent each of the statement mathematically;
[tex]y = 3z...eq(i)\\x = 2z ...eq(ii)\\[/tex]
Let's substitute the values and find the value of angle C
[tex]a + b + c = 180\\2z + 3z + z = 180\\6z = 180\\z = 30\\c = 30^0\\b = 90^0\\a = 60^0[/tex]
From the calculations above, the value of a, b and c are 60 degrees, 90 degrees and 30 degrees respectively.
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solve this problem pls
Which equation represents the line shown in the graph below?
The equation that represents the graphed line is y = -3x + 2. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The kine is passing through (0, 2) and (1, -1). Then the slope of the line is given as,
m = (2 + 1) / (0 - 1)
m = -3
And the y-intercept of the line is 2. Then the equation of the line is given as,
y = -3x + 2
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The complete question is attached below.
3/10 +1/4 + 4/5 =
answer in the simplest form
3/10 +1/4 + 4/5 = 27/20
the smallest score in a population is x = 5 and the largest score is x = 10. based on this information, you can conclude that the____.
Based on the information that the smallest score in a population is x=5, and the largest score is x=10, the conclusion is that the standard deviation is going to be smaller than the range of scores.
Given that in a population, the smallest score is x=5, and largest score is x=10, the range of scores is:
Range of scores=largest score-lowest score
=10-5
=5
Here the range of scores is 5, and the mean of the scores is likely to be between 5 and 10
Standard deviation which refers to the average spread of the distribution, will now be considered to be smaller since the range of scores is low.
Because standard deviation is found from the mean, if the mean is between x=5 and x=10, the standard deviation must be lower than x=5.
Hence, smaller than the range of scores.
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Which number sentence is true? A. 8.565 < |-13.23| B. 7/8 < 0.78 C. 4/11 < -4.11 D. 23.5 < 2 3/5
Answer:
A
Step-by-step explanation:
beacuse the rest are false
Can anyone help me with this?
The line shown in the graph have slope of line as 13/27 with rise 13 and run 27.
What is slope of line?
The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in comparison to other lines shown on the same coordinate plane.
The formula to calculate the slope of any line is given by:
[tex]slope = \frac{rise}{run}[/tex]
We know that, '
rise = y₂ - y₁
run = x₂ - x₁
As we can see in the graph
x₂ = 10, y₂ = 3
x₁ = -7, y₁ = -10
putting the values in above formula
rise = y₂ - y₁ = 3 -(-10) = 13
run = x₂ - x₁ = 10 -(17) = 27
so, slope = 13/27
Hence the slope of the line shown in graph is 13/27.
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The table of values below shows the amount of water in a watering can and the weight of the can. Based on this information, how much does a gallon of water weigh?
Amount of Water in Can (gallons) Weight of Cans (pounds)
0 2
0.5 6.2
1 10.4
1.5 14.6
2 18.8
A
4.2 pounds
B
6.2 pounds
C
8.4 pounds
D
10.4 pounds
Each gallon of water weighs by itself is 8.4 pounds, option (C) 8.4 pounds is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
From the data given:
When the Amount of Water in Can (gallons) = 0
Weight of Cans (pounds) = 2
It means the weight of the can = 2 pounds
For the 0.5 gallons, the weight of the can = 6.2 pounds
For the 0.5 gallons, the weight of the water = 6.2 - 2 = 4.2 pounds
For the 1 gallon, the weight of the water = 2x4.2 pounds
= 8.4 pounds
Thus, each gallon of water weighs by itself is 8.4 pounds, option (C) 8.4 pounds is correct.
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Write an equation of the line that passes through the given point and has the given slope. (−5, 4); slope −3
Answer:
y = -3x - 11
Step-by-step explanation:
Slope = -3
so...
-3x
y = -3x + (b)
given : (-5, 4) x=-5 y=4
4 = -3(-5) + b
4 = 15 + b
b = -11
so...
y = -3x - 11
Please help, thank you to who ever does
Answer:
-6
Step-by-step explanation:
