Step-by-step explanation:
x varies directly as y
x=ky
12=4k
k=12/4
k=3
1. The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
2. A savings account is opened with an initial deposit of $425.00. Determine the account balance after 9 years if the account earns 2.7% simple interest annually.
$3,928.28
$1,457.75
$528.28
$103.28
3. An arithmetic sequence begins with 56, 59, 62, 65, 68, …
Which option below represents the formula for the sequence?
f(n) = 56 + 3(n − 1)
f(n) = 53 + 3(n − 1)
f(n) = 56 + 3(n)
f(n) = 53 + 3(n + 1)
4. The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. Solve for r.
r = 0.04
r = 0.14
r = 0.26
r = 0.40
1. In the simple interest equation, 687.5 = 550(1 + 0.05t), A. The value 550 represents the initial balance in the account, which means the account started with $550.
2. The account balance of a savings account opened with an initial deposit of $425.00, after 9 years if the account earns 2.7% simple interest annually, is C. $528.28.
3. The formula for the arithmetic sequence which begins with 56, 59, 62, 65, 68, … is C. f(n) = 56 + 3(n).
4. The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account, where r is A. r = 0.04.
What is the simple interest system?The simple interest system operates without compounding the interest.
Compounding implies that interest attracts interest.
1) 687.5 = 550(1 + 0.05t)
Principal = $550
Final amount after t years = $687.50
Simple interest rate = 0.05 or 5%
Time, t = [$687.5/$550 - 1]/0.05
= 5 years
2) Principal = $425.00
Time = 9 years
Simple interest rate = 2.7%
Amount after 9 years = $528.28 ($425 x 1 + (9 x 2.7%)
3) Arithmetic Sequence:f(n) = 56 + 3(n)
Where n = 1:
f(n) = 56 + 3(1)
= 56 + 3
= 59
Where n = 2:
f(n) = 56 + 3(2)
= 56 + 6
= 62
4) Principal = $600
Amount after 9 years = $816
Simple interest rate = r
r = ($816/$600 - 1)/9
= 0.04
= 4%
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Answer:
Answer below
Step-by-step explanation:
1. The value 550 represents the initial balance in the account, which means the account started with $550.
2. (C) 528.28
425.00 x 2.7% x 9 = 103.275
Then we add 103.275 to the initial deposit of $425.00
425.00 + 103.275 = 528.275
Therefore the answer is (C) 528.28
3. The answer for this one is (A) f(n) = 56 + 3(n − 1)
So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex] .
Therefore, its 56 + 3(n − 1)
4. For this one we solve for r and using a calculator its (A) r = 0.04
5. Oh also he doesn't have this one but its (C) 102
An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. How many seats are in the 10th row?
60
93
102
110
As we can see the common difference is 8.
Then we use the rule for nth term which is [tex]a_{n} =a_{1} +d(n-1)[/tex]
[tex]a_{n} =30+8(n-1)[/tex]
[tex]a_{n} =30+8n-8[/tex]
[tex]a_{n} =22+8(10)[/tex]
[tex]a_{n} =22+80[/tex]
[tex]a_{n} = 102[/tex]
So therefore, the answer is (C) 102.
Find the number that makes the ratio equivalent to 6:1.
?:10
Answer:
60
Step-by-step explanation:
?=60, multiply each side of the ratio by 10 to get the answer
6×10:1×10
60:10
a line passes through point (2,-6) and has a slope of -9. write an equation in ax+by=c form for this line. use integers for a,b, and c.
// lol please help :,) //
Answer:
9x +y = 12
Step-by-step explanation:
You want the standard form equation for the line with slope -9 through the point (2, -6).
Point-slope formThe point-slope form equation is a good place to start when given a point and a slope. That equation is ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y -(-6) = -9(x -2) . . . . line with slope -9 through point (2, -6)
Standard formThis can be rearranged to the desired form:
y +6 = -9x +18 . . . . . . eliminate parentheses
9x +y = 12 . . . . . . . . add 9x -6
A triangle with the coordinates A (-5, 2), B (1, 3), and C (-5, -8) is dilated with a scale
factor of 5 with the origin as the center of dilation. What are the coordinates of B'?
22fl oz/ minutes ≈ mL/s
After the conversion of 22 fl oz/minutes to mL/s, we get 10.41 mL/s
What is fluid ounce(fl oz)?
The fluid ounce is different from the (international avoirdupois) ounce as a unit of weight or mass, even though it is occasionally referred to as simply "one ounce" when the context clearly indicates what is meant. There is almost exactly one ounce of pure water in one imperial fluid ounce of volume.
A fluid ounce, often known as a capacity or fl oz, is a volume measurement unit that is frequently used to measure liquids.
An imperial fluid ounce is exactly 28.4130625 milliliters (1/20 of an imperial pint, 1/16 of an imperial gallon).
As, 1 fl oz = 28.41 mL
∴ 22 fl oz = (28.41×22) mL
⇒ 22 fl oz = 625.02 mL
Since, 1 minute = 60 s
∴ 22 fl oz/minutes = (625.02/60) mL/s
⇒ 22 fl oz/minutes = 10.41 mL/s
After the conversion of 22 fl oz/minutes to mL/s, we get 10.41 mL/s
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the perimeter of a square is 48 centimeters, what is the area in square centimeters
Answer:
144cm²
Step-by-step explanation:
If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.
48/4 = 12cm
Then, to find the area, you need to multiply 12 by 12.
12 cm x 12 cm = 144cm²
Hope this helps :)
8 (a) The formula for the area of a trapezium is A = = h(c + d)
(* Find an expression for c in terms of A, hand d.
The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
What is the area of the trapezium?
The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.
To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:
A = h(c + d)/2
2A = h(c + d)
2A/h = c + d
c + d = 2A/h
Then, we can subtract d from both sides of the equation to solve for c:
c = (2A/h) - d
Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
What is the area of the trapezium?
The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.
To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:
A = h(c + d)/2
2A = h(c + d)
2A/h = c + d
c + d = 2A/h
Then, we can subtract d from both sides of the equation to solve for c:
c = (2A/h) - d
Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
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Help help help help pls
a )The equation of the new parallel line is x - y = 3
b ) The equation of the new perpendicular line is x + y = -1
What are the equations of the new parallel and perpendicular lines?The given line passes through the points (0, 3 ) and (-3, 0).
Here,
[tex](x _{1}, y _{1}) = (-3, 0)\\\\(x _{2}, y _{2}) = (0, 3)[/tex]
The slope of the line = m
[tex]m =\frac{y_{2}- y _{1}}{x _{2}- x_{1}} \\\\m = \frac{3-0}{0+3} \\\\m = \frac{3}{3} = 1[/tex]
The slope of the given line is 1
a ) The new line passes through the point (1, -2) and is parallel to the given line .
So, the slope remains the same , m = 1The point- slope form of the equation is given by ,[tex]y- y_{1} = m (x- x_{1}) -- (1)[/tex]
Substituting ( [tex]x _{1}, y_{1}[/tex] ) = (1, -2) and m = 1 in (1) ,y + 2 = 1 (x -1 )
y +2 = x - 1
x - y -1 -2 = 0
x - y - 3 =0
x - y = 3
The equation of the new parallel line is x - y = 3
b ) The new line passes through the point (1, -2) and is perpendicular to the given line .
So, the slope of the new line is the negative reciprocal of the slope of the given line , m = - 1The point- slope form of the equation is given by ,[tex]y- y_{1} = m (x- x_{1}) -- (1)[/tex]
Substituting ( [tex]x _{1}, y_{1}[/tex] ) = (1, -2) and m = -1 in (1) ,y + 2 = -1 (x -1 )
y +2 = - x + 1
x + y -1 +2 = 0
x + y + 1 = 0
x + y = -1
The equation of the new perpendicular line is x + y = -1
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Question 1 (1 point)
How many solutions does the system of equations have?
Answer: 0
Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.
What can use the distributive property to the algebraic expression 5(x - 7)
Usibg the distributive property to the algebraic expression 5(x - 7) will be 5x - 35.
What is distributive property?The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.
When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you want to multiply 5 by the product of 10 plus 3. When two terms are similar, we typically add the two numbers before multiplying by 5. However, the property states that you should first multiply each addend by 5.
Therefore, 5(x - 7) will be:
= 5(x) - 5(7)
= 5x - 35
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7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
[tex]xvertex = -b / 2a[/tex]
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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Explain Harvey's error in the following scenario.
Harvey's sow has just delivered five piglets. The veterinarian has examined the mother and babies, the
piglets have nursed, and it is time for everyone to get some rest. Harvey has filled the pen with clean, dry
straw, and he puts all the pigs in the pen to spend their first night together.
Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.
How should we treat a newborn pig?When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.
Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.
Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.
According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.
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7
10
1
2/5
Cedric has
3
of the pie
of the pie
of the pie
of the nie
4
of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
C
PR
The fraction of the pie left that each friend will receive is; 3/8 of the pie
How to divide fractions?Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.
The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.
For example, 3/8 divided by 3/4 would be;
3/8 divided by 3/4 = 3/8 * 4/3
Now, we are told that cedric has 3/4 of a pie left.
Now, he wants to share equally among two of his friends, it means that;
Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8
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Complete question is;
Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?
Bob is a member of a gym. He paid a joining fee, plus a monthly fee. The equation below represents the amount he has paid as a function of the number of
months he has been a member of the gym. Interpret the slope of the function in terms of the problem.
y=22m +39
A. Bob pays $39 for 22 months.
B. Bob pays $22 per year.
C. Bob pays $22 per month
D. Bob pays $39 per month
Bob pays $22 per month as 39 is joining fee which is only for first month
What is an example of a slope intercept form?
Slope-Intercept Form Examples
Example 1: Assuming a line has a slope of 1/2 and intersects the y-axis at (0, -3). Find the line's equation. Y = x/2 - 3 is the solution to the line's equation. Example 2: Using the horizontal line slope intercept formula, determine the equation at which the y-axis intersects (0, 8).
How is a slope equation solved?
Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily see the slope.
Given that:
y=22m+39
Slope of the function is 22 and it is membership fee of a month .
If bob wants to increase membership for a months , he has to pay 22 extra and joining fee of 39
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the owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. she randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. what are the null and alternative hypotheses for this hypothesis test?
The null and different hypotheses for hypothesis test are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
Null hypotheses
Null hypothesis is usually what researchers or scientists try and confute, and if the null hypothesis is accepted, we have a tendency should modification our opinion, i.e., we have a tendency should modification our original opinion or statement so as to match the null hypothesis. H0 denotes the null hypothesis.Given that:
sample size (η)= 196
sample proposition (p^) = 114/196
Let p denote the population proportion of people who use a loyalty card.
The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]
Hence, the null and alternative hypothesis are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
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Given OP bisects angle MON, PM is perpendicular to PM and PN is perpendicular to ON. Prove PN is congruent to PM
1. [tex]\overline{OP}[/tex] bisects [tex]\angle MON[/tex] (given)
2. [tex]\angle MOP \cong \angle PON[/tex] (definition of angle bisector)
3. [tex]\overline{PN} \perp \overline{ON}[/tex], [tex]\overline{PM} \perp \overline{OM}[/tex] (given)
4. [tex]\angle PNO[/tex] and [tex]\angle PMO[/tex] are right angles (definition of perpendicular lines)
5. [tex]\angle PNO \cong \angle PMO[/tex] (all right angles are congruent)
6. [tex]\overline{OP} \cong \overline{OP}[/tex] (reflexive property)
7. [tex]\triangle MOP \cong \triangle NOP[/tex] (AAS)
8. [tex]\overline{PN} \cong \overline{PM}[/tex] (CPCTC)
It is proved that PN is congruent to PM by CPCTC
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
We are Given OP bisects angle MON, PM is perpendicular to PM and PN is perpendicular to ON.
Therefore, Angle PNO and Angle PMO are right angles ( by definition of perpendicular lines)
All right angles are congruent;
Triangle PNO is congruent to Triangle PMO
OP = OP (by reflexive property)
Thus, MOP is congruent to NOP by AAS
PN = PM (CPCTC)
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alyssa has $75 less than three times eric together they have $905 how much money do they each have
Alyssa has the money of worth $660
Eric has the money of worth $245
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the amount Alyssa has.
Let y be the amount Eric has.
alyssa has $75 less than three times eric
=> x= 3y - 75
Together they have $905
=> x + y =905
Substitute x
=> 3y - 75 +y = 905
4y = 905 +75 = 980
y = 980 /4 = 245
x= 3y - 75 = 3(245) - 75 = 660
Alyssa has $660
Eric has $245
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PLEASE HELP NEED TO ANSWER SO I DONT HAVE TO TAKE A MIDTERM EXAM
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.4 meters thick.
Let y represent the ice sheet's thickness (in meters) after x weeks.
Complete the equation for the relationship between the thickness and number of weeks.
y=______
The linear equation that relates the thickness and the number of weeks is:
y = -0.2*x + 3.36
How to find the equation for the thickness?We know that the thickness decreases at a constant rate of 0.2 meters per week, so we will have a linear function between y, the thickness, and x, the number of weeks:
y = -0.2*x + b
Where b is the initial thickness
We know that after 7 weeks the sheet is 2.4 meters thick, so we can write:
2.4 = -0.2*7 + b
Now we can solve this for b.
2.4 + 0.2*7 = b
3.36 = b
Then the linear equation is:
y = -0.2*x + 3.36
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In a recent poll, 45% of adults took 2 weeks' vacation in 2017, and 23% of adults took 2 weeks' vacation and went out of the country. What is the probability that an adult went out of the country given they took 2 weeks' vacation?
The probability that an adult went out of the country given they took 2 weeks' vacation is 51%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that in a recent poll, 45% of adults took 2 weeks' vacation in 2017, and 23% of adults took 2 weeks' vacation and went out of the country.
The probability will be calculated as,
Probability = (23 / 45) x 100
Probability = 0.51 x 100
Probability = 51%
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at the city museum, child admission is $5.30 and adult admission is $9.80. on thursday, 143 tickets were sold for a total sales of $1149.40. how many adult tickets were sold that day?
The number of adult tickets which were sold that day as calculated from the given data is 29.
First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.
To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.
This is represented by the following equation,
$8.90A + $5.30C = $928
Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:
3 * C = A
Now we can answer our first problem by substituting 3 * C for A.
8.9 (3C) + 5.3C = 928
26.7C + 5.3C = 928
32C = 928
C = 29
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The video game club lost 8 members which was 28% of their group.
What was the original attendance of the video game club?
HELP!!!
The original attendance of the video game club was 28.57 members.
To determine the original attendance of the video game club, you can use the following formula:
Original attendance = (Number of members lost) / (Percent of group that left)
Plugging in the values from the problem, we get:
Original attendance = (8 members) / (28%)
To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:
Original attendance = (8 members) / (0.28)
Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:
Original attendance = 28.57 members
Therefore, the video gaming club had 28.57 members when it first started.
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A worker in a silver mine descends 26 feet use an integer to represent the change in the workers position
Answer: -26 feet
Step-by-step explanation:
Match the Vocab Word to the definition.
Remember, you are allowed to use your notes to help you!
Question 3 options:
If a = b, and c ≠ 0, then a/c = b/c
If a = b, then a + c = b + c
If a > b, and c > 0, then a/c > b/c
If a > b, and c < 0, then a/c < b/c
If a > b, then a - c > b – c
If a = b, then c ∙ a = c ∙ b
If a > b, and c > 0, then c ∙ a > c ∙ b
If a > b, and c < 0, then c ∙ a < c ∙ b
If a = b, then a - c = b - c
If a > b, then a + c > b + c
1.
Addition Property of Equality
2.
Subtraction Property of Equality
3.
Multiplication Property of Equality
4.
Division Property of Equality
5.
Addition Property of Order
6.
Subtraction Property of Order
7.
Multiplication Property of Order
8.
Division Property of Order
Match the Vocab Word to the definition
1. Addition Property of Equality
If a = b, then a + c = b + cIf a > b, then a + c > b + c2. Subtraction Property of Equality
If a = b, then a - c = b - cIf a > b, then a - c > b – c3. Multiplication Property of Equality
If a > b, and c > 0, then c ∙ a > c ∙ bIf a > b, and c < 0, then c ∙ a < c ∙ bIf a = b, then c ∙ a = c ∙ b4. Division Property of Equality
If a = b, and c ≠ 0, then a/c = b/cIf a > b, and c > 0, then a/c > b/cIf a > b, and c < 0, then a/c < b/cWhat is order property in math?Order property refers to situation of changing the order of the factors. swapping the positions of the addends still maintain the answer
For instance commutative property of addition
a + b = b + acommutative property of multiplication
a * b = b * aThe properties of equality refers to performing same operation in the opposite sides of an equation
Addition Property of Equality: here c is added to both sides of the equality such that a = b, then a + c = b + c
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Find the amount with the same value as:
70 x 7-2
A
0
B
14
C
149
D
17
The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numerical expression is given below.
⇒ 70 / (7 - 2)
Simplify the expression, then we have
⇒ 70 / (7 - 2)
⇒ 70 / 5
⇒ 14
The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.
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The correct expression is given below.
70 / (7 - 2)
this exercise uses the population growth model. the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) estimate how long it takes the population to double. (round your answer to two decimal places.) yr (b) estimate how long it takes the population to triple. (round your answer to two decimal places.) yr
a) The estimated population which takes time to get double is 63.36.
b) The estimated population which takes time to get triple is 100.42.
The growth equation is A(t) = [tex]A_0e^{kt}[/tex] where A(t) is the quantity at time t, A₀ is the initial quantity, k is a positive constant, and [tex]e^{(x)}[/tex] is the natural exponential function. For A₀ = 7.1E9 (7.1 billion) and k = 0.011 (1.1%):
Given formula:
A(t) = [tex]A_0 e^{kt}[/tex] --------------------------- (1)
A(t) = [tex]7.1E9e^{0.011t}[/tex] ----------------------------(2)
a) We have to find twice the population, or if A(t) = 2A₀. For doubles (or multiples of A₀₎, equation (1) can be written as
A(t) = [tex]A_0e^{0.11t}[/tex]
⇒ 2A₀ = [tex]A_0e^{0.11t}[/tex], (replaces A(t) = 2A₀)
⇒ 2 = [tex]e^{0.011t}[/tex],
⇒ ln(2) = ln(e0.011t ),
⇒ ln(2) = 0.011t,
⇒ ln(2)/0.011 = t
Therefore,
t = 63.36
b) Now we will find the number of years it will take the population to be triple of its size.
7.1 × 3 = [tex]7.1(1.011)^t[/tex]
⇒ [tex]\frac{7.1 * 3}{7.1}[/tex] = [tex]1.011^{t}[/tex]
⇒ 3 = [tex]1.011^{t}[/tex]
Now, Using the logarithm:
ln(3) = ln [tex](1.011)^{t}[/tex]
⇒ t = 100.42
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Which parent function is represented by the graph?
O A. An exponential parent function
• B. The quadratic parent function
• C. The absolute value parent function
O D. The linear parent function
Parent function is represented by the graph is
B. The quadratic parent function
What is Parent function?
A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.
A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.
The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.
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in a class of 40 students, 20 have examination scores below 77% and 20 have scores above 77%. which measure(s) of central tendency can you immediately determine?
Observing the information provided and using concept of central tendency parameters of statistics, The central tendency which we can immediately determine is median.
What is statistics?A field of mathematics that deals with gathering, analyzing, interpreting, and presenting vast amounts of numerical data.
What do you mean by measure of central tendency?The statistical test that determines whether a single result accurately represents a whole distribution is known as measure of central tendency.
total students = 40.
half = 20 students.
20 have scores below 77% and 20 have above 77%.
Thus, We can immediately determine that the median of score is 77%.
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fillings how much do prices vary for filling a cavity? to find out, an insurance company randomly selects 10 dental practices in california and asks for the cash (non-insurance) price for this procedure at each practice. the interquartile range is $74.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.
2. The insurance company then computes the interquartile range of the prices for each practice.
3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.
The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.
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what is the correct congruence statement for triangles shown
Answer:
It is NLJ
Step-by-step explanation:
Trust me lol
help me asapp!! i dont know much about this stuff
Answer:
D
Step-by-step explanation:
Take the coefficients of each term and list them.
- 1 5 - 9
Multiply 3 by the first coefficient and combine it from the second.
- 1 * 3 = - 3, 5 - 3 = 2
Multiply 3 by this product and combine it from the third term.
3 * 2 = 6, - 9 + 6 = - 3
Your remainder is option D, - 3.
Answer:
-3
Step-by-step explanation:
3 -1 5 -9
-3 6
-1 2 3
Remainder: -3
Factored: [tex]-x+2-\frac{3}{x-3}[/tex]
1.) Set up the synthetic division.
2.) drop the first term down. My teacher used to say "drop it like its hot" :)
3.) Multiply c by the value just written on the bottom row.
4.) Add the column created in step 3.
5.) Repeat until done.
6.) Write out the answer
