[tex]A=Pe^{rt} \\ \\ 15000000=10000000e^{12r} \\ \\ 1.5=e^{12r} \\ \\ \ln(1.5)=12r \\ \\ r=\frac{\ln(1.5)}{12} \\ \\ r \approx \boxed{0.0338}[/tex]
The exponential growth rate of the population of the country is given by the relation r = 1.8595 %
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the initial population of the country in 2010 be = 12 million
Let the final population of the country in 2022 = 15 million
Now , let the growth rate be represented as r
And , growth rate r = [ ln( final population - ln (initial population ) / no of years ] x 100
Growth Rate = (ln(15 ) - ln(12 )) / (2022 - 2010)
r = (2.70805 - 2.48491) / 12
r = 0.018595
r = 1.8595 %
Hence , the growth rate r = 1.8595 %
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Find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.
The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.
Let l be the length and w be the width of the rectangular garden.
We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.
The perimeter of the rectangular garden = 300 meters
We know that the perimeter of the rectangle =2(length + width)
300 = 2(l + w)
l + w = 150 .......(1)
Now, the maximum area of a rectangular garden is when Length = width
So, for equation 1
l + l = 150
l = 75 meters
So, w = 75 meters
And the area of the rectangular garden = length * width
= 75 * 75
= 5625 m²
So the maximum area of the rectangular garden is 5625 m²
Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is 5625 m²
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Let’s say you are viewing a confidence interval plot and you notice a horizontal line placed at each end of the line (ex. similar to this image T). What does this horizontal line signify?
Select an answer:
These horizontal lines allow Minitab to properly place the dot.
These horizontal lines are used to decorate the plots.
These horizontal lines indicate the limits at the end of the intervals.
These horizontal lines are placed to help you visually locate the dot.
The thing that the horizontal line signifies in the confidence interval plot is D. These horizontal lines are placed to help you visually locate the dot.
What exactly is a confidence interval?A confidence interval is a range of values that contains the value of an unknown population parameter. Given the characteristics of your sample data, these intervals represent a plausible domain for the parameter.
Confidence intervals are calculated using a specified confidence level and are derived from sample statistics. Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. These horizontal lines are placed to assist you in visualizing the dot.
In conclusion, the correct option is D.
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Use the image given below to answer the next two questions.
The quadrilateral below, JKLM, is a rhombus.
Find the value of each angle listed below.
Note: Do not include the ° sign in your answer.
m∠JKL
Applying the properties of a rhombus, the value of each angle listed are:
m∠JKL = 72°
m∠MLK = 108°
m∠JMK = 36°
m∠MJL = 54°
m∠KNL = 90°
What is a Rhombus?A rhombus is a quadrilateral with the following properties:
All its sides are congruent.Its opposite angles are equal.Its adjacent angles are supplementary, they have a sum of 180 degrees.The diagonals bisect the angles.The diagonals bisects each other at right angles.Rhombus have opposite sides that are parallel to each other.Given, m∠JKM = 36°, apply the properties of a rhombus to solve the missing values.
m∠JKL = 2(36)
m∠JKL = 72°
m∠MLK = 180 - 72 [adjacent angles are supplementary in a rhombus]
m∠MLK = 108°
m∠JMK = 36°
m∠MJL = 1/2(m∠MLK)
m∠MJL = 1/2(108)
m∠MJL = 54°
m∠KNL = 90° [bisection of the diagonals of a rhombus at right angles).
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a farm has 22 cows and chicken altogether. Each cow has four legs, and each chicken has two legs. The farmer counted 62 legs total. How many cows are on the farm? How many chickens?
The number of cows are 9 and the number of chickens are 13.
Given that, a farm has 22 cows and chicken altogether.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let the x be the number of cows and y be the number of chicken.
Now, x+y=22 -------(I)
The farmer counted 62 legs total.
So, 4x+2y=62 -------(II)
Multiply equation (I) by 2, we get
2x+2y=44 -------(III)
Subtract equation (III) from equation (II), we get
4x+2y-(2x+2y)=62-44
⇒ 2x=18
⇒ x=9
Substitute x=9 in equation (I), we get
9+y=22
⇒ y=13
Hence, the number of cows are 9 and the number of chickens are 13.
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Use the formula A=P\left(1+r/n)^nt to solve the compound interest problem.
Find how long it takes a 1700$ investment to earn 500$ interest if it is invested at 2% interest compounded quarterly.
500$ interest will be earned in approximately years. (Round to the nearest tenth.)
The total years taken to double the money according to Compounding will be 13.75 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 2%
amount = $1700
Total amount = $2200
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/400)^4t
T = A[tex](1+r/400)^{4t[/tex]
2200 = 1700(1 +2/400)^4t
22/17 = (1 +1/200)^4t
22/17 = (1.005)^4t
1.29 = (1.005)^4t
taking log on both sides
0.11/0.002 = 4t
t = 13.75 years.
Hence the time taken to double the money is 13.75 years.
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Suppose that 11 inches of wire costs 33 cents. At the same rate, how much (in cents) will 5 inches of wire cost?
Answer:
15 cents
Step-by-step explanation:
[tex]\frac{11}{33} =\frac{5}{y}[/tex]
Cross Multiply.
11 · y = 5 · 33
11y = 165
11y ÷ 11 = 165 ÷ 11
y = 15
What is the sum of the roots of the equation
Answer:
-2.5
Step-by-step explanation:
For a quadratic equation [tex]ax^2 + bx+c=0[/tex], the sum of the roots is [tex]-b/a[/tex].
Here, [tex]b=5[/tex] and [tex]a=2[/tex], so the sum is [tex]-2.5[/tex].
Write an inequality that describes the safe speeds to drive according to the sign.
Speed Limit 65
Minimum 45
Paul is making picture frames. He wants to make at least 8 picture frames and needs 24.5 inches of material for each frame.
Write an inequality that can be used to determine how much material, x, Paul should buy.
An inequality that can be used to determine how much material, x, Paul should buy is x ≥ 196.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.
Given:
Paul is making picture frames.
He wants to make at least 8 picture frames and needs 24.5 inches of material for each frame.
To find the total material for 8 frames:
Multiply by 8 to material for one form
24.5 x 8
= 196 inches
To write an inequality that can be used to determine how much material, x, Paul should buy:
x ≥ 196 inches.
To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more.
You must flip the inequality sign if you multiply or divide either side by a negative number.
Therefore, the inequality is x ≥ 196.
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To raise funds for the local animal shelter, a group of BYU-Idaho students sold collars and scratching posts. The first week they sold seven collars and 10 scratching posts and donated $299.83. The second week they sold nine collars and 18 scratching posts and donated $482.85. "Because it is difficult to make two different items, they want to sell only one item during the last two weeks of the fundraiser. They decide to sell only the item for which they can donate the most money per item sold.
By using simultaneous linear equation, it can be concluded that-
They should sell only scratching post during the last two weeks of the fundraiser
Third option is correct
What is simultaneous linear equation?
At first, it is important to know about linear equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of simultaneous linear equation needs to be solved
Let the cost of one collar be $x and the cost of one scratching post be $y
The first week they sold seven collars and 10 scratching posts and donated $299.83.
7x + 10y = 299.83 ..... (1)
The second week they sold nine collars and 18 scratching posts and donated $482.85.
9x + 18y = 482.85 .... (2)
Multiplying (1) by 9 and (2) by 5
63x + 90y = 2698.47 ..... (3)
45x + 90y = 2414.25 ... (4)
Subraction (4) from (3)
18x = 284.22
x = [tex]\frac{284.22}{18}[/tex]
x = $15.79
Putting the value of x in (1)
7 [tex]\times[/tex] 15.79 + 10y = 299.83
110.53 + 10y = 299.83
10y = 299.83 - 110.53
10y = 189.3
y = [tex]\frac{189.3}{10}[/tex]
y = $18.93
Since the cost of one scratching post is more than cost of one collars, they should sold scratching post during the last two weeks of the fundrasiser
Third option is correct
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Complete Question
The complete Question has been attached
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer: False
Step-by-step explanation:
1. Find the volumes of the spheres below.
Answer:
= about 1436.75504
Step-by-step explanation:
V = 4/3 π r³
The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees?
A. 000–250
B. 001–250
C. 0–250
D. 1–250
The correctly labels the population of employees is, 001 - 250.
What is population?
The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.
Given:
The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale.
He decides to use a random number table to survey a simple random sample of 50 of the 250 employees.
As the population consist of 250 employees and simple random sample of size 50, to use a random number table to survey a sample random sample of 50 of the 250 employees, the population of employees should be labeled as 001-250.
Hence, the correctly labels the population of employees is, 001 - 250.
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In triangle ABC, segment AD is perpendicular to segment BC, and segment AC, is perpendicular to segment BA.
Based on the information in the diagram, what is the length of segment DC?
Step-by-step explanation:
based on the geometric mean theorem
h² = pq
h = height of the main right-angled triangle.
p and q are the segments of the baseline of the main right-angled triangle.
12² = 36x
144 = 36x
x = 144/36 = 4
so, DC is 4 units long.
what goes in the question marks?
OPTIONS:
1. Corresponding angles
2. definition of parallel lines
3. substitution property of equality
4. reflexive angles
5. segment bisector
By using the properties of parallel lines, it can be inferred that -
Corrosponding angle goes in the place of first question mark and substitution property of equality goes in the place of second question mark.
What are parallel lines?
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal is a line that intersects two or more parallel lines
For the first question mark
[tex]\angle ASR \cong \angle AVU[/tex] [Corrosponding angle]
For the second question mark
[tex]m\angle AVU = 90^{\circ}[/tex] [Substitution property of equality]
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Sweet Branch grocery sells 5 bottles of soda for $6. As of next week, though, the price per bottle will increase by 10% . How much will 12 bottles of soda cost next week?
12 bottles of soda cost $15.84 next week
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Price of 5 bottles = $6
Price of 1 bottle = 6/5 = $1.2
10% of 1.2 = (10/100)*1.2 = 0.12
new price of 1 bottle = 1.2+ 0.12 = $1.32
Price of 12 bottles = 12*1.32 = $15.84
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Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
16)
16) x2 + 8x +
A) x2 + 8x + 8 = (x + 64)2
C) x2 + 8x + 64 = (x+8)2
B) x2 + 8x + 4 = (x+16)2
D) x2 + 8x + 16 = (x+4)²
Answer:
D) [tex]x^2+8x+16=(x+4)^2[/tex]
Step-by-step explanation:
[tex]x^2+8x+(8/2)^2=x^2+8x+16=(x+4)^2[/tex]
Drag numbers to the table so it shows a proportional relationship between and .
i need this all right please! im doing this for a grade and i really need this 100!!!.
Solving proportional relationship and options given we have value of x in second row as 5 and in third row as 8, value of y in third row as 2.4
What is proportional constant ?
The ratio between two proportional quantities' constant values is known as the constant of proportionality.
When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.
The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.
To show proportional relationship we need to have [tex]\frac{y}{x}[/tex] as a constant value k.
From first set of data, we can have our constant k as
[tex]k=\frac{.6}{2} =0.3[/tex]
Now to fill 2nd row of table we have value of y given and as discussed above [tex]\frac{y}{x}[/tex] will remain constant. So, solving we get
[tex]x = \frac{1.5}{0.3} = 5[/tex]
So, value of x in second row will be 5
For third row we can substitute as value of x as 8 and value of y as 2.4 that will give us proportional constant as calculate in above cases.
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if the area of the trapezoid is 70 square unites what is the length CE
the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are
what is area?Area is a mathematical concept that expresses the size of a region on a planar or curved surface. A shape's "space enclosed within the perimeter or the boundary" is referred to as its area. Math formulas are used to determine the area of various forms.
given
area of the trapezoid is 70 units
and the 1st base = 20 units and 2nd base = 10 units
length CE ?
area of trapezoid = 1/2( b1 + b2)*h
70= 1/2 (20 + 10 )*h
70 = 1/2(30)*h
h = 4.6 units
the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are
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Simplify roots of negative numbers -14
Step-by-step explanation:
since it's -14 then it will be√-14
√-14=√-2 multiplied is by √7
so that will be √-2√7
You invest $3,600 in a savings account that earns simple interest of 3%, how much money is in your account after 5 years?
Answer:
$4,140.00
Step-by-step explanation:
Interest = principle x rate x time
I = 3600 x .03 x 5
I = 540
Add the interest to what is already in the account
540 + 3600
4140
10 point question and brainliest
two people need to answer for me to give brainliest
Landscape Elementary uses 14 reams of paper every 3 weeks. How many reams of paper do they use each week? Round the answer to the nearest hundredth and do not include a label.
Answer:
4.67 (nearest hundredth)
Step-by-step explanation:
In 3 weeks, Landscape Elementary uses 14 reams of paper.
In 1 week, Landscape Elementary uses 14/3 reams of paper. = 4.66666...
The digit at thousandth place is 6 and it is more than 5. Thus add 1 with hundredth digit.
4.66666... = 4.67 (nearest hundredth)
Express in scientific notation and then solve.
There was a total of $9.48 million contributed to a political campaign by 79 thousand
people. What was the average contribution?
Answer:
the average contribution to the political campaign was $0.12.
Step-by-step explanation:
To find the average contribution to the political campaign, we first need to convert the total amount of money contributed and the number of people who contributed to scientific notation.
The total amount of money contributed to the political campaign was $9.48 million, which can be written in scientific notation as $9.48 * 10^6.
The number of people who contributed to the campaign was 79 thousand, which can be written in scientific notation as 79 * 10^3.
To find the average contribution, we need to divide the total amount of money contributed by the number of people who contributed. Therefore, we can substitute the values in scientific notation into the formula to find the average contribution:
Average contribution = Total amount / Number of people
= 9.48 * 10^6 / 79 * 10^3
= 9.48 / 79
= 0.12
Therefore, the average contribution to the political campaign was $0.12.
Please help me with this problem
a) The Test statistic of the hypothesis is; 0.23
b) The p-value from the test statistic is; 0.409
c) The final conclusion is there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.
How to find the test statistic?Test statistic is defined as a number, calculated from a statistical test, used to find if your data could have occurred under the null hypothesis. In this case, we are dealing with proportions and as such the test statistic has the formula;
z = (p1 - p2)/standard error
p1 = 14/167 = 0.084; s1 = √(0.084 * 0.916/167) = 1.285
p2 = 316/833 = 0.38; s2 = √(0.38 * 0.62/833) = 0.0168
Hence, for the distribution of differences, the mean and the standard error are given as follows:
Mean: p = 0.38 - 0.084 = 0.296
Standard error: s = √(1.285² + 0.0168²) = 1.2854
a) Test statistic = p/s = 0.296/1.2854
Test statistic = 0.23
b) From p-value from z-score calculator, we get that;
p-value = 0.409
c) The p-value is greater than the significance value of 0.04, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.
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At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.? (Round your answer to three decimal places.)
The speed (in km/hr) of the ships changing at 4.00pm is 20.62km/hr
How to calculate speed in a journey?The given parameters are;
The distance between A and B = 170km=m
The distance between B and C is 30km=m
Time is 12.00 noon to 4.00 pm = 4 hours
From the given parameters,
m=170-35*4 = 170-140=30
The Distance (D)=√(30²+120²
D=30*√(1²+4²)
Simplifying to get
30√17
From the Pythagoras theorem,
D²=m²+n²
Applying differential calculus,
⇒2m(dm/dt)+2n(dn/dt)=2D(dD/dt)
Applying the figures from the question we have
2*30*(-35)+2*120*30=2*30√17*dD/dt
Simplify to get
120-35=√17dD/dt
This implies that dD/dt=85/√17
⇒5√17=20.6155281km/h
Therefore, the speed between the ships is ≅20.62km/hr
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Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specific point.2(x-2)^2 + (y-1)^2 + (z-3)^2 = 10 at (3,3,5,)(a) x+y+z=11(b) x-3=y-3=z-5
For the given surface ;
(a) the equation of the tangent is x + y + z = 11 ,
(b) equation of normal is (x - 3) [tex]=[/tex] (y - 3) = (z - 5) .
In the question ,
it is given that ,
the equation of the surface is 2(x-2)² + (y-1)² + (z-3)² = 10 ,
we have to find the equation of the tangent at (3,3,5) .
the partial derivative fₓ = 4(x -2)
[tex]f_{y}[/tex] = 2(y-1) and [tex]f_{z}[/tex] = 2(z-3) .
the partial derivatives at (3,3,5) will be fₓ = 4(3 -2) = 4
[tex]f_{y}[/tex] = 2(3-1) = 4 and [tex]f_{z}[/tex] = 2(5-3) = 4 .
Part(a)
the equation of tangent at the point (3,3,5) is
fₓ(x - x₁) + [tex]f_{y}[/tex](y - y₁) + [tex]f_{z}[/tex](z - z₁) = 0 ,
Substituting the values form above ,
we get ,
4(x-3) + 4(y-3) + 4(z-5) = 0
4x - 12 + 4y - 12 + 4z - 20 = 0
after simplifying , we have 4x + 4y + 4z = 44 .
dividing both sides by 4 ,
we get ,
x [tex]+[/tex] y [tex]+[/tex] z [tex]=[/tex] 11 .
Part(b) ,
the equation of Normal is ;
(x-x₁)/fₓ = (y-y₁)/ [tex]f_{y}[/tex] = (z-z₁)/ [tex]f_{z}[/tex]
(x - 3)/4 = (y - 3)/4 = (z - 5)/4
(x - 3) [tex]=[/tex] (y - 3) [tex]=[/tex] (z - 5)
Therefore , the equation of tangent is x + y + z = 11 , and equation of normal is (x - 3) = (y - 3) = (z - 5) .
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What is the area of the rectangle shown on the coordinate plane?
7.14 unit² is the area of the rectangle shown on the coordinate plane
What is the area of rectangle?The length and breadth of the rectangle multiplied together provide the area of the rectangle. To determine the area occupied by a rectangle within its perimeter, we compute the area of the rectangle.
Consider rectangle with vertices A(-1,-2), B(-3,-4), C(-6,-1) and D(-4,1). The area of the rectangle is:
Area = length × width
Now, find the length and the width:
Length (BC) = [tex]\sqrt{[-3-(-6)]^2 + [(-4)-(-1)]^2}[/tex]
or, BC = [tex]\sqrt{(3)^2 +(-3)^2}[/tex]
or, BC = [tex]\sqrt{18}[/tex] unit
Width (AB) = [tex]\sqrt{[(-1) -(-3)]^2 + [(-2)-(-4)]^2}[/tex]
or, AB = [tex]\sqrt{(2)^2 +(2)^2}[/tex]
or, AB = [tex]\sqrt{8}[/tex] unit
Then the area of the rectangle ABCD is
Area(ABCD) = length (BC) × width (AB)
or, Area(ABCD) = [tex]\sqrt{18} *\sqrt{8}[/tex]
or, Area(ABCD) = 7.14 unit²
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How to subtract fractions with different denominators? Please explain step by step
Answer: 20/48
(simplified) 5/12
Step-by-step explanation:
We will use 6/8 - 2/6 for our example
6/8 - 2/6
Multiply the denominator on the right side by the denominator on the left side: 6x8 = 48
Make 48 the denominators on both sides: /48, /48
Now multiply the denominator on the left side with the numerator on the left side: 6x6 = 36
Make the first fraction's numerator 36: 36/48
Now multiply the denominator on the left side by the numerator on the right side: 8x2 = 16
Now make 16 the numerator of the second fraction: 16/48
Now that the denominators are the same, we can subtract!
36/48-16/48 = 20/48
Now to simplify:
divide 20/48 by 4 = 5/12
So the answer is 20/48 and when it is simplified it comes out to 5/12
This is how you subtract fractions with different denominators.
You can use the same method when adding, the only difference is that instead of adding in the last step, you add instead!
(TONS OF POINTS AND BRAINLYEST GURANTEE) Please answer the question that is stated in the image below. Thank you. It really means a lot to me.
Answer:
Below
Step-by-step explanation:
a) All possible rolls ( 36 of them)
1 1 , 2 , 3 , 4 , 5 , 6
2 1, 2, 3, 4, 5 , 6
3 1 , 2 , 3 , 4,5,6
4 1,2,3,4,5,6
5 1,2,3,4,5,6
6 1,2,3,4,5,6
b) underlined above 21 out of 36 or 7/12
c ) 3 out of 36 1/12
d ) 11/36
The ratio of of distance between two places A and B and B to C is 4:5. If the distance between A to C is 72 km, find the distance between A to B.
the whole distance containing all three points will be AC, and we know that AC = 72 km, now point B is between splitting the AC segment into AB and BC to a 4 : 5 ratio.
well, hell for that let's simply grab the total amount of 72 and split it up by dividing it by (4 + 5) and distribute accordingly.
[tex]A\stackrel{\text{\LARGE 4}}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\text{\LARGE 5}}{\rule[0.35em]{14em}{0.25pt}} C \\\\\\ \stackrel{AB}{4}~~ : ~~\stackrel{BC}{5} ~~ \implies ~~ \stackrel{AB}{4\cdot \frac{72}{4+5}}~~ : ~~\stackrel{BC}{5\cdot \frac{72}{4+5}} \\\\\\ \stackrel{AB}{4\cdot 8}~~ : ~~\stackrel{BC}{5\cdot 8} ~~ \implies ~~ \stackrel{AB}{\text{\LARGE 32}}~~ : ~~\stackrel{BC}{40}[/tex]