The volume of the composite figure can be divided into two separate figures: a cylinder and a half-sphere, with the total volume being 108 cubic centimeters.
What is the exact volume of the composite figure?The composite figure can be divided into two separate figures: a cylinder and a half-sphere.
The formula for the volume of a cylinder is:
Volume of the cylinder = π[tex]r^2[/tex]h, where r is the radius of the cylinder and h is the height of the cylinder.
In this case, the radius of the cylinder is 3 centimeters and the height of the cylinder is 10 centimeters, so the volume of the cylinder is:
Volume of the cylinder = π[tex](3cm)^2(10cm)[/tex] = 90π [tex]cm^3[/tex]
The formula for the volume of a half-sphere is:
Volume of half-sphere = (2/3)π[tex]r^3[/tex], where r is the radius of the half-sphere.
In this case, the radius of the half-sphere is also 3 centimeters, so the volume of the half-sphere is:
Volume of half-sphere = (2/3)π[tex](3cm)^3[/tex] = 18π [tex]cm^3[/tex]
To find the total volume of the composite figure, we add the volume of the cylinder and the volume of the half-sphere:
Total volume = Volume of cylinder + Volume of half-sphere
Total volume = 90π [tex]cm^3[/tex] + 18π [tex]cm^3[/tex]
Total volume = 108π [tex]cm^3[/tex]
Therefore, the exact volume of the composite figure is 108π cubic centimeters.
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What is 24/32 reduced as much as possible?
Answer:
3/4
Step-by-step explanation:
Hope this helps! Pls give brainliest!
A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees Fahrenheit, for those months. The scatter plot shows the data
The statements that are true are:
(A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.
(D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.
(E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
Using the function A(t) = -1.4t + 96, we can determine the amount of oil, A, used in gallons for a given average temperature, t, in degrees Fahrenheit.
A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.
Substituting t = 10 into the function A(t), we get:
A(10) = -1.4(10) + 96 = 80
Therefore, the statement is true.
B) The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.
Substituting t = 15 into the function A(t), we get:
A(15) = -1.4(15) + 96 = 76.5
Therefore, the statement is false.
C) The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.
Substituting t = 68.5 into the function A(t), we get:
A(68.5) = -1.4(68.5) + 96 = -2.9
Therefore, the statement is false.
D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.
Substituting t = 55 into the function A(t), we get:
A(55) = -1.4(55) + 96 = 18
Therefore, the statement is true.
E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
Substituting t = 0 into the function A(t), we get:
A(0) = -1.4(0) + 96 = 96
Therefore, the statement is true.
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The given question is incomplete, the complete question is:
A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees
Fahrenheit, for those months. The scatter plot shows the data. The function A(t) = -1.4t + 96, best fits these data.
Graph- (25,60), (40,40),(45,40),(55,20),(60,10)
Use the function to determine which of the following statements are true. Select all that apply.
A- The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.
B- The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.
C- The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.
D- The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.
E- The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
sunset lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. assuming logistic growth with a carrying capacity of 25000, find the growth constant , and determine when the population will increase to 12900.
The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.
We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,
The logistic growth model is given by the equation
dN/dt=rN[(K-N)/K]
where, dN/dt = rate of change of population with respect to time,
N = population size at time t,
r = intrinsic rate of natural increase (growth constant),
K = carrying capacity.
The population size, "N" after 1 year = 7050
The initial population, "N₀" = 2500
The carrying capacity, K = 25000
We can use the following formula to find the value of the growth constant,
r = 2.303/t{ln(N_t/N₀) }........... (1)
Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)
Substituting the given values in equation (1), we get
r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69
The value of the growth constant is 0.69.
Now, we can use the logistic growth equation to find the time required for the population to reach 12900.
dN/dt=rN[(K-N)/K]
Given, N₀ = 2500 and K = 25000
Differentiating both sides with respect to t,
dN/dt = rN[(K-N)/K] + Ndr/dt
Substituting the values of N, r, and K in the above equation, we get,
dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}
Let the population N become 12900 at time t = t₁
Therefore, at time t = 0, the population N₀ = 2500
Also, at time t = 1, the population N₁ = 7050
Substituting these values in the above equation, we get,
dN/dt= 0.69N[(25000-N)/25000] + N₁
dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁
Solving for N₁, we get, N₁ = 7825
Substituting N₁ = 7825 in the above equation,
dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁
dN/dt= 3263.25/1.69 ⇒ 1930.4
Now, to find t1, we can use the following formula;
ln[(K-N₁)/(K-N₀)] = rt₁
Substituting the given values, we get,
ln[(25000-12900)/(25000-2500)] = 0.69t₁
On solving for t₁, we get;
t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years
Hence, the population will increase to 12900 after approximately 3.7 years.
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ivy received a bank statement reposrting the recent changes to her account. the statement showed an overall increase in the account balance of $1,692.45. during the time shown on the statement, ivy was paid twice and withdrew a total of $1,876.23 to cover all her bills and expenses. how much (x) is each of ivay's paychecks? help me please
if Ivy received two Paychecks during the time period shown on the statement, each paycheck would be $1,784.34.
To find out how much each of Ivy's paychecks is, we need to subtract the amount she withdrew from her account from the overall increase in her account balance.
So, the calculation would be:
Overall increase in account balance - Total amount withdrawn = Total amount deposited
$1,692.45 - $1,876.23 = -$183.78
This means that Ivy actually spent more than she earned during the time period shown on the statement. Therefore, we cannot determine the amount of each of her paychecks with the given information.
However, if we assume that Ivy did not have any other income or expenses during the time period, we can use the following equation:
2x - $1,876.23 = $1,692.45
where x is the amount of each paycheck.
Simplifying the equation, we get:
2x = $3,568.68
x = $1,784.34
Therefore, if Ivy received two paychecks during the time period shown on the statement, each paycheck would be $1,784.34.
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Mr Cobb says that increasing something by 10% then decreasing it by 10% will just give you the original amount. Mr Pathuis says the new amount will be bigger. Mr Drake says the new amount will be smaller. Who is right and why?
Answer:
Mr Drake is right.
Step-by-step explanation:
Because you first decreased it by 10% of the ORIGINAL value.
You then increased it by 10% of the DECREASED value.
The percentages are the same percentages, but on different base amounts.
Simple example:
$100 decreased by 10% of $100 ($10) is $90.
$90 increased by 10% of $90 ($9) is $99.
Answer:
Mr Drake Is correct
Step-by-step explanation:
When you increase something by 10%, you multiply the original value by 1.1. When you decrease it by 10%, you multiply the increased value by 0.9. So the final amount is:
original value x 1.1 x 0.9 = 0.99 x original value
Therefore, the new amount will be slightly smaller than the original amount, and Mr. Drake is correct.
Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?
The probability of drawing an odd number or a multiple of 3 is 1/5.
What is probability?Probability is simply the chance that something will happen.
Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome.
Analyzing events according to their probabilities is called statistics.
So, the given data set is:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
Odd multiples of 3 are 3 and 9.
Then, the probability would be:
P(E) = 2/10
P(E) = 1/5
Therefore, the probability of drawing an odd number or a multiple of 3 is 1/5.
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42. Let P(A)=0.70,P(B∣A)=0.55 , and P(B∣A C )=0.10 . Find the following probabilities: a. P(A C ) b. P(A∩B) and P(A C ∩B) c. P(B) d. P(A∣B) 43. Complete the following probability table.
Here is the probability table to be completed: A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45
42. Let P(A) = 0.70, P(B∣A) = 0.55, and P(B∣AC) = 0.10. The following probabilities are found: a. P(AC) = 0.30 b. P(A∩B) = P(B∣A) × P(A) = 0.55 × 0.70 = 0.385 P(AC∩B) = P(B∣AC) × P(AC) = 0.10 × 0.30 = 0.03 c. P(B) = P(B∣A) × P(A) + P(B∣AC) × P(AC) = 0.55 × 0.70 + 0.10 × 0.30 = 0.415 d. P(A∣B) = P(B∣A) × P(A) / P(B) = 0.55 × 0.70 / 0.415 = 0.9289 43. Here is the probability table to be completed: A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45
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Nicole is a wedding organiser. The guests sit at a circular table with a diameter of 180cm each guest needs 7cm around the cicumference of the table. Their are 18 tables at the venu. There is a toptal of 145 guests. Are their enoughb tables
From the given data of Nicole's wedding organization, 18 tables at the venue is sufficient for the total 145 arriving guest.
To determine whether there are enough tables for the guests, we need to calculate the total circumference required for all the guests and compare it to the total circumference of the available tables. The circumference of a circle is given by the formula C = πd, where C is the circumference, d is the diameter, and π is the constant pi, approximately equal to 3.14.
For the circular table with a diameter of 180cm, the circumference is:
C = πd
= π x 180cm
= 565.2cm
Each guest needs 7cm around the circumference of the table, so the total circumference required for one guest is 7cm.
For 145 guests, the total circumference required is:
Total circumference required
= 145 guests x 7cm per guest
= 1015cm
Now, we can calculate the total circumference of all the tables available:
Total circumference of all tables
= 18 tables x 565.2cm per table
= 10,174.4cm
Since the total circumference required for the guests (1015cm) is less than the total circumference of all the available tables (10,174.4cm), we can conclude that there are enough tables for the guests. Therefore, there are enough tables at the venue for the 145 guests.
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Which is the smallest?
(a) -1,
(b) -1/2,
(c) 0,
(d) 3.
Answer:
A
because it is a negative number and because it is less than -1/2
Answer:
Step-by-step explanation:
the answer is -1 as negative integers become smaller as they go to the left.
no problem
240
Use the ratio 1. What operation can you do on both terms to find
an equivalent ratio that has 1 as the second term?
Answer:
You need to first identify the dum it's always multiplication
hope this helps good luck
Select whether the equation has a solution or not. x-8+-/x2-8 roots no roots
The correct statement regarding the number of solutions of the equation is given as follows:
The function has one solution.
How to obtain the number of solutions?The function for this problem is defined as follows:
[tex]x - 8 = -\sqrt{x^2 - 8}[tex]
We can remove the term with x from the square root squaring both sides of the equality, hence:
[tex](x - 8)^2 = (-\sqrt{x^2 - 8})^2[/tex]
x² - 8 = x² - 16x + 64
16x = 72
x = 72/16
x = 4.5.
Hence the equation presented in this problem has a root, which is a solution, and the number of solutions is of one.
Missing InformationThe function is given as follows:
[tex]x - 8 = -\sqrt{x^2 - 8}[tex]
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JKLM is a rhombus. m/MLN = (9a + 11)° m /KLM = (-4a + 66)°
Find the m2KJM.
The value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).
What is rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is sometimes referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.
Let us suppose the measure of angle = x.
For rhombus all the four angles are congruent, thus,
∠MLN = (9a + 11)°
∠KLM = (-4a + 66)°
∠JLN = x
∠KLJ = x
The sum of the angles of a quadrilateral is 360 degrees, so:
∠JKL + ∠KLM + ∠MLN + ∠NJL = 360
Since JKL and NJL are vertical angles, they are congruent:
∠JKL = ∠NJL = x
Substituting in the given angles, we get:
x + (-4a + 66) + (9a + 11) + x = 360
2x + 5a + 77 = 360
2x = 360 - 5a - 77
2x = 283 - 5a
x = (283 - 5a)/2
Now, ∠JKM = 180 - ∠JKL
∠JKM = 180 - x
∠JKM = 180 - (283 - 5a)/2
Simplifying, we get:
∠JKM = 23 + (5a/2)
Hence, the value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).
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A right circular cylinder has the dimensions shown below.
r = 17.2 yd h = 45.3 yd
What is the volume of the cylinder? Use 3.14 for tr. Round to the nearest tenth and include correct units.
Show all your work.
42080.9 cubic yd
Step-by-step explanation:
Volume of right circular cylinder:r = 17.2 yd
h = 45.3 yd
[tex]\boxed{\bf Volume=\pi r^2h}[/tex]
= 3.14 * 17.2 *17.2 * 45.3
=42080.9 cubic yd
Question :-
What is the volume of a right circular cylinder with a radius of 17.2 yd and a height of 45.3 yd?Answer :-
The volume of a right circular cylinder is 42080.873 yd³.[tex] \rule{180pt}{4pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{17.2 \: yd}}\put(9,17.5){\sf{45.3 \: yd}}\end{picture}[/tex]
Solution :-
As per provided information in the given question, we have been given that the Radius of a cylinder is 17.2 yd. The height of a cylinder is 45.3 yd. We have been asked to find the volume of a right circular cylinder.
To calculate the volume of a right circular cylinder, we will apply the formula below :-
[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: Volume_{(Cylinder)} = \pi r^2 h \: \: }}[/tex]
Substitute the given values into the above formula and solve for Volume :-
[tex]\sf:\implies Volume_{(Cylinder)} = \pi r^2 h[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(17.2 \: yd)^2(45.3 \: yd)[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(295.84 \:yd^2)(45.3 \: yd)[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = (928.9376 \:yd^2)(45.3 \:yd)[/tex]
[tex]\sf:\implies\bold{Volume_{(Cylinder)} = 42080.873 \: yd^3}[/tex]
Therefore :-
The volume of a right circular cylinder is 42080.873 yd³.[tex]\\[/tex]
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Have a great day! <33
The area of the triangle below is 1/16 square centimeters. What is the length of the base. Express your answer as a fraction in simplest form
The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
What does fraction mean?A fraction is a mathematical expression which represents a part of a whole. It is written as a ratio that compares two numbers, the numerator and denominator. The numerator indicates the number of parts, the denominator indicates the total number of parts that make up the whole. Fractions can be expressed as decimals, percentages, and other forms of representation.
To solve this problem, we must use the formula for area of a triangle. This formula states that the area of a triangle is equal to one-half the product of the base and the height. In this problem, the area of the triangle is given as 1/16 square centimeters. This means that the base times the height must equal 1/8.
To find the length of the base, we must isolate the base from the equation. To do this, we must divide both sides of the equation by the height. This will leave us with the equation base = 1/8/height. Since the height is unknown, we can solve for it by taking the reciprocal of the base. This will give us the equation height = 1/8/base.
Combining both equations, we can solve for the base by multiplying both sides of the equation by 1/8. This will give us the equation base = (1/8)(1/8) = 1/64. The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
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What is the area?
6 ft:
6 ft
10 ft
square feet
Step-by-step explanation:
6x6x10 FT = 1 sq cube foot
Add the number that would make the expression a perfect square. Next, write an
equivalent expression in factored form. Do not put spaces in your answers.
1. X2 + 3x+
= (x+
2. X2 + 0. 6x+
= (x+
a) We need to add 2.25 to the expression to make it a perfect square and equivalent expression is (x + 1.5)^2.
b) We need to add 0.09 to the expression to make it a perfect square and equivalent expression is (x + 0.3)^2.
a) To make the expression X^2 + 3x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 3 is 1.5, and 1.5 squared is 2.25.
X^2 + 3x + 2.25 = (x + 1.5)^2
The equivalent expression in factored form is (x + 1.5)^2, which represents a perfect square trinomial.
b) Similarly, to make the expression X^2 + 0.6x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 0.6 is 0.3, and 0.3 squared is 0.09. Therefore, we need to add 0.09 to the expression to make it a perfect square:
X^2 + 0.6x + 0.09 = (x + 0.3)^2
The equivalent expression in factored form is (x + 0.3)^2, which represents a perfect square trinomial.
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3⋅5 1 +2 can anyone help with this I really tried my best and I've been hard working at this but I'm still stuck at it
35 1 + 2 = 17. To remember the mathematical operations in the correct order, people frequently use the abbreviation PEMDAS.
You must follow the order of operations, often known as PEMDAS, to evaluate this equation. Parentheses, exponents, multiplication and division (left to right), addition, and subtraction are all referred to as PEMDAS (from left to right).
When using PEMDAS, you would first calculate the output of the parenthesized expression—which is 3 times 5—and then add 2.
Thus, 35 1+2 reduces to:
3*5 1 + 2 = (3*5) + 2 (first calculate within the parentheses) = 15 + 2 (conduct multiplication) = 17 (perform addition)
Hence, 35 1 + 2 = 17.
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help me bro help me bro help me bro help me bro help me bro
By writting all the numbers as decimals we can see that the lake that lost the least amount of water is the last one.
Which lake lost the least amount of water?The first lake lost a fraction of 5/6 of its total water.
The second lake lost the 85% of its water.
The last lake lost a fraction of 246/300 of its water.
We want to see which of these 3 numbers is the smaller one, we can write all of them as decimals ot get:
5/6 = 0.833
85% = 0.85
246/300 = 0.82
With this we conclude that the lake that lost the least amount of water is the last one.
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Hey can someone help me pleaseeee SOLVE WITH EXPLANATION!!! >:(
This is the same information as you’ll use in the next question.
The equation for the period of a pendulum is given by T space equals space 2 straight pi square root of straight L over 32 end root where T is the time (in seconds) and L is the length of the pendulum (in feet).
Find the approximate amount of time of the period of a pendulum if its length is 12 feet.
The approximate amount of time period of a pendulum with a length of 12 feet is 1.85 seconds.
What is calculus?Calculus is a branch οf mathematics that deals with the study οf change and hοw things change οver time.
We can use the given equatiοn fοr the periοd οf a pendulum:
T = 2π√(L/32)
Substituting L = 12, we get:
T = 2π√(12/32)
Simplifying:
T ≈ 1.85 seconds
Hence, the approximate amount of time of the period of a pendulum with a length of 12 feet is 1.85 seconds.
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Trinagle abc is similar to triangle def. The following ratios of corresponding sides are equal. 8/10 = 16/20 = 4x+6/4x+11
The value of x is 0. This means that [tex]8/10 = 16/20 = 4x+6/4x+11[/tex], so the corresponding sides of triangles abc and def have the same ratio.
The similarity of two triangles can be determined by the ratio of their corresponding sides. In the case of triangles abc and def, the ratio of corresponding sides is [tex]8/10 = 16/20 = 4x+6/4x+11[/tex].
To calculate the value of x, we can use the first two ratios and cross-multiply. With 8/10 = 16/20, we get 8*20=16*10, which simplifies to 160=160. Therefore, the first two ratios are equal.
To calculate the value of x using the third ratio, we can use the same method. With 4x+6/4x+11, we get ([tex]4x+6)*(4x+11)=4x^2+44x+66[/tex]. This simplifies to [tex]4x^2+44x+66=4x^2+44x+66[/tex], so the third ratio is also equal.
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Complete question:
What is the value of x in the ratio 8/10 = 16/20 = 4x+6/4x+11?
Create an exponential equation passing through points (1960, 179323175) and (2010, 308745538) Round (a) and (b) to 3 decimal places
The exponential function passing through the points (1960, 179323175) and (2010, 308745538) is given as follows:
y = 0.1(1.01092581)^x.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients a and b are explained as follows:
a is the initial value.b is the rate of change.The points for this problem are given as follows:
(1960, 179323175) and (2010, 308745538).
Considering that between 1960 and 2010 there is an increase of 50 in the input, the parameter b is obtained as follows:
b^50 = 308745538/179323175
b = (308745538/179323175)^(1/50)
b = 1.01092581.
Hence:
y = a(1.01092581)^x.
When x = 1960, y = 179323175, hence the parameter a is obtained as follows:
a = 179323175/[(1.01092581)^1960]
a = 0.1.
Hence the function is:
y = 0.1(1.01092581)^x.
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Jason read a total of 8 books over 4 months. If Jason has read 16 books so far, how many months has he been with his book club? Solve using unit rates. its worth 100 points
Answer:
8 months
Step-by-step explanation:
I got it right
Which expression has a value of 15 when p=12
Answer: p+3
Step-by-step explanation:
if p=12 and you need the answer to be 15, all you need to do is find 12+_= 15. Since 12+3=15 your answer would be p+3.
The graph shows the predicted population of a town, z number of years after 2020. According to the graph, which statement is true?
According to the graph, the true statement is the population will increase more each year than the previous year. The Option B is correct.
What does population increase means?in geography context, a population growth means the increase in the number of humans on Earth. In human history, the population size was relatively stable. But with innovation and industrialization, energy, food, water, and medical care became more available and reliable.
On this graph, we can observed how the population increases from 80,000 to 100,000, 120,000, 140,000, 160,000, 180,000, 200,000, 220,000. 240,000, 260,000 and 280,000 on the Y-Axis. Therefore, the statement that population will increase more each year than the previous year is true.
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Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
The length AB is 2.
The length A'B' is 3.
The image is smaller than the pre-image.
The scale factor is Three-halves.
The scale factor is Two-thirds.
For the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. Yet, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.
The distance formula for the coordinates is given as:
d(A, B) = |x1 - x2|
From the figure we observe that,
d(A, B) = |2 - 4|
d(A, B) = |-2|
d(A, B) = 2 units.
Hence, option A is correct.
Also, the length of A'B' is:
d(A', B') = |3 - 6| = |-3| = 3 units.
Hence, option B is correct.
The original shape is called the pre-image in a transformation (in this example, a dilation), and the transformed shape is called the image.
The third response is untrue since the picture is larger than the pre-image.
The scale factor of the images is:
2k = 3
k = 3/2.
Hence, option 4 is correct.
The last option is also false, as the scale factor is already determined.
Hence, for the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.
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The complete question is:
solve the following system of equation y=x^2-32 y=x+10
x=(17,4)^2+(−340,−80)+58y= y^2−20y+68
y=y^2−20y+68
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is
Choose...
.
This means that
Choose...
mm of rain falls every
Choose...
.
The slope of the line is
3
This means that
6mm
of rain falls every
1hr
Use the clues to crack the code the number is greater than ten the value of the ones digit is ten times the value of the tenths digit Code number (5, 5, 7,
Given that there is only one digit left and the sum is more than 10, the third digit must be 7, which it is. and the pass code to open anything it is guarding is 5 5 7, which may be inputted.
To decode the code, we know that the number is more than 10 and has three digits: . Moreover, we are aware that the value of the ones digit is 10 times that of the tenths digit. The code is 5 5 7, as may be inferred from the provided hints.
Given that the code contains two 5s, the first digit must be 5. As the value of the ones digit is 10 times that of the tenths number, the second digit must likewise be 5, which is 5. The number is bigger than 10, hence the third digit must be 7, as it is the only one still present.
In order to open whatever it is guarding, the code, which is 5 5 7, may be input.
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Simplify the square root of 7 divided by 20
The simplified fοrm οf the square rοοt οf 7 divided by 20 is:
(7 + 2√(35)) / (20 * (√(7) + 2√(5))).
What is the equivalent expressiοn?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο simplify the square rοοt οf 7 divided by 20, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by the cοnjugate οf the denοminatοr, which is √(7) + 2√(5):
(√(7)) / 20 = (√(7) / 20) * (√(7) + 2√(5)) / (√(7) + 2√(5))
Expanding the numeratοr using the distributive prοperty gives:
(√(7) * √(7) + √(7) * 2√(5)) / (20 * (√(7) + 2√(5)))
Simplifying the numeratοr gives:
(7 + 2√(35)) / (20 * (√(7) + 2√(5)))
Therefοre, the simplified fοrm οf the square rοοt οf 7 divided by 20 is:
(7 + 2√(35)) / (20 * (√(7) + 2√(5))).
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