The population of the country will be 1051 million in 2014
How to model the population of the country?The exponential model that describes the population of a country' in millions, t years after 2003 is given as:
A = 999.8 e0.002t
Rewrite the function properly as:
A = 999.8 * e^(0.002t)
When the population of the country is 1051 million, it means that:
A = 1051
Substitute the known values in the above equation
So, we have:
1051 = 999.8 * e^(0.002t)
Divide both sides by 999.8
1.0512 = e^(0.002t)
Take the natural logarithm of both sides of the equation
ln(1.0512) = ln(e^(0.002t)
Rewrite the equation as:
ln(e^(0.002t) = log(1.0512)
This gives
0.002t = log(1.0512)
Evaluate the logarithmic expression
0.002t = 0.0216
Divide both sides of the equation by 0.002
t = 0.0216/0.002
Evaluate the quotient
t = 10.8
Approximate 10.8 as 11
t = 11
11 years from 2003 is 2014
Hence, the population of the country will be 1051 million in 2014
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MN =7. Find AB.
3.5
10.5
14
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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An airplane is heading due north at 700 kph, and a wind blows at 60 kph in the direction s 45° e. what is the plane’s ground speed?
We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.
Given the following data:
Airplane speed = 700 kph.Wind speed = 60 kph.Angle = 45° due East.What is speed?Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).
Mathematically, speed can be calculated by using this formula;
Speed = distance/time
How to calculate the plane’s ground speed?In order to calculate the airplane’s ground speed, we would apply the law of cosine:
C² = A² + D² - 2(A)(D)cosθ
Substituting the given parameters into the formula, we have;
C² = 700² + 60² - 2(700)(60)cos45
C² = 434,203.03
C = √434,203.03
C = 658.94 kph.
In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.
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full of sand, the wagon weighs 100 pounds. If the wagon weighs 80 ounces when its empty, how much do the bags of sand weigh?
given,
wagon weight with sand = 100 pounds
wangon weight = 80 ounces ÷ 16 = 5 pounds
sand weight = 100 - 5 = 95 pounds//
180 divided in the ratio of 7:3:5
Answer:
Let , the constant factor be x so 3 X + 5 x + 7 x = 180
Step-by-step explanation:
Find out the value of x
7x+3x+5x=180
15x=180
x=180/15
x=12
now,
x=3 multiplied by 12=36
x=7 multiplied by 12=84
x=5 multiplied by 12=60
brainliest pls if u wannna
if you could help with all 4 questions that would be great pls answer if you know the RIGHT answer
Step-by-step explanation:
3. B
because the figure to the left of the y-axis yields the one to the right when you reflect it across y = x.
4. C
Flip either of the figures vertically across x = -1 which is their intersection point and you'll get the other.
5. D
it can't be clockwise because the x value of the vertices would have been negative. so it is 270° counterclockwise resulting in ( -y , x )
6. A
Similar to #4 which except this time, you flip it horizontally like how you lay a book or pick it up.
HELPPP ASAP 25PTS! Find the area of the shape
Answer:
480
Step-by-step explanation:
Which of the following are possible measures of the interior angles of a regular polygon? If possible, how many sides does the polygon have: 90°, 100°, 110° 125°,
150°, 175°.
Step-by-step explanation:
180(n-2)/n=90 ( this is the solution for the 90)
cross multiplying
180n-360=90n
180n-90n=360
90n=360
90n/90=360/90
n=4, the number of sides for the polygon with 90° is 4 sides
Solution for 100°
180(n-2)/n=100
180n-360=100n
180n-100n=360
80n=360
80n/80=360/80
n=4.5
Same applies to the rest 110°,125° ,150°,175°
PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answer:
5/52
Step-by-step explanation:
There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.
The data set below has a lower quartile of 13 and an upper quartile of 37.
1, 12, 13, 15, 18, 20, 35, 37, 40, 78
Which statement is true about any outliers of the data set?
The correct option regarding the outliers of the data-set is given by:
The greatest value, 78, is the only outlier.
How to use the quartiles of a data-set to identitfy outliers?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile with the first quartile.Measures that are more than 1.5 IQR from Q1 and Q3 are considered outliers.The IQR for this problem is:
IQR = 37 - 13 = 24.
Hence the bounds for outliers are:
Less than 13 - 1.5 x 24 = -23.Greater than 37 + 1.5 x 24 = 73,The options are:
No outliers.Only 1 is an outlier.Only 78 is an outlier.Both 1 and 78 are outliers.Hence the correct option is that only 78 is an outlier.
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What is the area of the parallelogram shown above
The area of the parallelogram is 55 square feet
How to determine the area of the parallelogram?From the figure, we have the following dimensions:
Height = 5 ft
Base = 11 ft
The area of the parallelogram is calculated as:
Area = Base * Height
This gives
Area = 5ft * 11ft
Evaluate the product
Area = 55 square feet
Hence, the area of the parallelogram is 55 square feet
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The volume of a sphere is 256/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.
the surface area of the sphere is π/4 cm^3
How to determine the surface areaIt is important to know the formula for surface area and volume of a sphere
Surface area = [tex]\frac{4\pi }{r^2}[/tex]
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
[tex]\frac{256}{3} \pi = \frac{4}{3} \pi r^3[/tex]
Pi cancels out and we have cross multiply to get the radius
[tex]256 * 3 = 4 * 3 r^3[/tex]
[tex]12r^3 = 768[/tex]
Make r the subject of the formula
[tex]r = \sqrt[3]{\frac{768}{12} }[/tex]
[tex]r = \sqrt[3]{64}[/tex]
r = 4
Let's substitute to find the surface area
Surface area = [tex]\frac{4\pi }{4^2}[/tex]
Surface area = π/4
Surface area = π/4 cm^3
Thus, the surface area of the sphere is π/4 cm^3
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Question 3 of
Select the correct answer.
A meteorologist observed the temperature in Clarkton over a two-year period. The graph below shows the average monthly
temperature in Clarkton during this period.
The function describing this graph is a transformation of the parent cosine function, y = cos(z).
Which interval is closest to the range of the transformed function ?
With respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.
How to find the functions corresponding to each graph based on the period of a function?Mathematically speaking, cosines are periodic functions, and period (T) is the distance in the horizontal axis such that f(t + T) = f(t). The period of the parent cosine function is 2π. The period in daughter functions may vary by means of the following form:
y = cos Ax (1)
Where:
x - Independent variable
y - Dependent variable
A - Period width
From the graph, it is observed that with respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.
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Answer: The answer is [0,65]
Step-by-step explanation:
60. In the given figure, PTR is tangent of a circle. If AT=PT and ZAPT=20°, what is the value of ZABT?
The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
A circle is shown in the picture.
PTR is the tangent of a circle.
AT=PT
Angle APT=20°
Let O is the center of the circle:
Angle BOT = 2 Angle PAT = 40 degrees
BO = TO = r
Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees
RTP is the tangent
OT ⊥ PTR
Angle OTA = 90 - Angle ATR = 50 degrees
Angle ABT = 180 - Angle PAT - Angle BTA
= 180 - 20 - (170 + 50)
= 40 degrees
Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
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20 POINTS
Data Analysis and Probability - Computing mean absolute deviation from a list of numerical values
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15
Answer:
2.571428
Step-by-step explanation:
The mean absolute deviation of a dataset is the average distance between each data point and the mean.
Paulo wants to buy new carpet for his bedroom. The floor is in the shape of a rectangle. Its length is 16 feet and its width is 11 feet. The carpet he wants costs $9 per square foot. How much will the carpet cost for the floor?
Answer:
11x9=99 16x9=144=243 144+99
The cost of the carpet required for the given rectangular floor is $1584.
A rectangle is a quadrilateral with equal pairs of sides.
Given that:
The shape of the floor is a rectangle.
The length of the floor is 16 feet.
The width of the floor is 11 feet.
So,
The area of the floor = length × breadth
= 16 × 11
= 176 sq feet
The area of the floor is 176 sq feet.
The cost of the carpet for a 1 sq foot floor = $9
The cost of the carpet for a 176 sq feet floor = $9 × 176
= $1584
Thus, the cost of the carpet for a 176 sq feet floor is $1584.
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,320 ft Determine the flag's width and length if the length is 400 ft
greater than the width.
The flag's width is
_? ft. Its length is
_? ft.
Answer: 380 ft and 780 ft
Step-by-step explanation:
We can assume that the flag is a rectangle. If the width of the flag is w, then the length is w + 400.
The formula for the perimeter of a rectangle is [tex]2(l+w)[/tex]. Let's plug in the values we know.
[tex]P=2(l+w)\\2320=2(w+400+w)\\1160=2w+400\\760=2w\\w=380[/tex]
We know that the length is 400 more than the width, so let's find the length.
[tex]l=w+400\\l=380+400=780[/tex]
Hence, the flag's width is 380 ft and the length is 780 ft.
Matt (180lb male) goes to a party and is served beer in a 16 oz red plastic cup. he has 3 cups of beer over a two hour period. What is Matt's BAC?
Matt's BAC the equation for is mathematically given as
X= 4 standard drinks
This is further explained below.
What is Matt's BAC?Blood Alcohol Content, sometimes known as BAC, is a measurement that expresses the amount of alcohol present in the blood as a percentage. Because it is measured in grams per 100 milliliters of blood, a blood alcohol concentration (BAC) of 0.08 indicates that your blood contains 0.08 percent alcohol by volume.
Generally, One standard drink is equal to twelve ounces of beer.
He drank a total of 48 ounces of beer since he had three cups of beer that were each 16 ounces.
In conclusion, the number of standard drinks that Matt consumed
X= 48/12
X= 4 standard drinks
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Find the surface area of the prism.
Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centered at a=1. Write the Taylor series in summation notation
Answer:
[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Step-by-step explanation:
Taylor series expansions of f(x) at the point x = a
[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]
This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.
[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]
[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]
[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]
[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]
Substituting the values in the series expansion gives:
[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]
Factoring out e⁴:
[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]
Taylor Series summation notation:
[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]
Therefore:
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
State the converses of the following statements. In each case, also decide whether the converse is true or false.
(1) If n is an even integer, then 2n + 1 is an odd integer.
(2) If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
(3) If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
(4) If the decimal expansion of a real number is terminating, then the number is rational.
Help!
Answer:
See below.
Step-by-step explanation:
Converse
The converse of a statement is formed by switching the hypothesis and the conclusion.
Hypothesis: The part after the "if".Conclusion: The part after the "then".Question 1Given statement: If n is an even integer, then 2n + 1 is an odd integer.
Hypothesis: "n is an even integer"Conclusion: "2n + 1 is an odd integer"Converse: If 2n + 1 is an odd integer, then n is an even integer.
Question 2Given statement: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
Hypothesis: "a transversal intersects two parallel lines"Conclusion: "each pair of corresponding angles is equal"Converse: If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.
Question 3Given statement: If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
Hypothesis: "each pair of opposite sides of a quadrilateral is equal"Conclusion: "the quadrilateral is a parallelogram"Converse: If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.
Question 4Given statement: If the decimal expansion of a real number is terminating, then the number is rational.
Hypothesis: "the decimal expansion of a real number is terminating"Conclusion: "the number is rational"Converse: If a real number is rational, then the decimal expansion of the number is terminating.
Find the surface area of the cone to the nearest square unit. Use π = 3.14.
6 cm
3 cm
The surface area of the cone exists as πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
How to find the surface area of the cone?
The surface of the cone consists of the lateral surface and the base area. So,
1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.
2. the base area exists πr² (since the base exists a circle with radius r).
Then the surface area exists SA = πrs + πr²
The surface area of the cone exists as πr² + πrl
where "r" exists the radius, "l" exists the slant height
The radius of the cone exists at 6 cm
The slant height of the cone exists at 3 cm
To find the surface area of a cone
The surface area of a cone = πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
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Geometry question need help finding the answer.
Answer: 1208.96
Step-by-step explanation:
The volume of the cylinder is [tex](\pi)(4^2)(4)=64\pi[/tex]
The volume of the prism is [tex](6)(12)(14)=1008[/tex]
So, the total volume is [tex]1008+64\pi=\boxed{1208.96}[/tex]
the vertex of this parabola is at (-5,-2) when the x value is -4 the y value is 2 . what is the coefficient of the squared expression in the parabola's equation
The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.
What is the vertex coefficient of the equation of the parabola?
In this question we must find the vertex coefficient of the equation of the parabola, which is the vertex form of the quadratic equation:
y - k = C · (x - h)²
If we know that (h, k) = (- 5, - 2) and (x, y) = (- 4, 2), then the vertex coefficient is:
2 - (- 2) = C · [- 4 - (- 2)]²
4 = C · (- 2)²
C = 1
The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.
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Sarah attempt to convert 8 miles in to kilomiters explain her error and then provide a correct conversion
Answer:
12.8 km
Step-by-step explanation:
each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km
1. Use the figure to determine the value of x and y.
Answer:
Step-by-step explanation:
x=100 bc like 180-80=100
y=80 bc vertical angles
Answer:
y = 80*
x = 100*
Step-by-step explanation:
y is the same to the 80* angle and therefore x is 100*
180* - 80 = 100*
How do I solve it I am running low on time it says it wrong don’t know
x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.
Solve the inequality:The inequality can be solved as the same way as we solve an algebraic equation.
Combine the terms with variables to one side and constants to other side.To multiply the whole inequality with negative terms we reverse the sign of the inequality.Here in the question the inequality to be solved is given:
- 3x + 7 < 4
By subtracting 7 from both sides of the inequality we get,
⇒ - 3x + 7 - 7 < 4 - 7
⇒ - 3x < - 3
To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,
we get,
⇒ 3 x > 3
Now finally by dividing the whole inequality by 3 we get,
⇒ x > 1
The number line representation can be done by marking values from 1 to numbers greater than 1.
Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.
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Which of the following is NOT a monomial? -11x
x - 4
3
22xy
Answer:
x - 4
Step-by-step explanation:
monomial is one term
-11x is only one term
x-4 isn't
3 is one term
22xy is only one term
only x-4 isn't a monomial
If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
0 A. 3x2 + 6
OB. 5x²-6
OC. 5x²-4
OD. 3x² - 4
Answer:
Option A is correct.
3x^2+6
Step-by-step explanation:
We have to find (f-g)(x):
We can write it f(x)-g(x), so substitute the values:
f(x)-g(x)=(4x^2+1)-(x^2-5)
=4x^2+1-x^2+5
=3x^2+6
A large container holds 4 gallons of chocolate milk that has to be poured into 1-pint bottles. if the ratio of gallons to pints is 1 : 8, how many bottles are needed? a. 2 bottles b. 4 bottles c. 8 bottles d. 32 bottles e. 40 bottles
32 bottles are needed to poured 4 gallons of chocolate milk.
The correct option is D.
What do you know about volume?A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.
According to the given information:Pints to Gallons Ratio: 1:8
Permit x bottles to be present.
There are x bottles required for 4 gallons of chocolate milk.
Because of the direct proportion
4/x = 1/8
x = 4 x 8
x = 32
As a result, 32 bottles are required.
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Find the length of the line joining the points A(-2,10) and B(-8,2)
Length of the line
= [tex]\sqrt{((-2)-(-8))^{2}+(10-2)^{2} }[/tex]
= [tex]\sqrt{36+64}[/tex]
=[tex]\sqrt{100}[/tex]
= 10