Answer:
l(n) = 80n + 520
Step-by-step explanation:
From the information given in the question, there is a relationship between the number of new policy sold, n, and earning, I
For 3 new policies, he earned $760
For 5 new policies, he earned $920.
The rate of change of IIya's earning with respect to number of new policy sales is
[tex]m = \frac{dI}{dn}[/tex]
[tex]m = \frac{920 - 760}{5 - 3}[/tex]
m = $160 / 2 policies
m = $80 / policy
The linear equation for the relationship is;
l(n) = mn + b
I(n) is Ilya’s weekly income which is a function of the number of new policies, n
m is the rate of change of I with respect to n
n is the number of new policies,
b is the intial function which is IIya's income when n equals zero
Recall, Ilya earns a commission of $80 for each policy sold during the week. (m = $80 per policy)
l(n) = 80n + b
To complete the relationship l, we need to calculate the initial value b.
For 3 new policies, he earned $760,
760 = 80(3) + b
760 = 240 + b
b = 760 - 520
b = 520
The final equation is l(n) = 80n + 520
From the final equation, we can deduce that Ilya’s weekly salary is $520 and he earns an additional $80 commission for each new policy sold.
Final answer:
Ilya's weekly income I(n) can be determined by constructing an equation from the two given points of data, namely I(3) = $760 and I(5) = $920. By solving the system of linear equations, we find that Ilya's base salary is $520 and his commission per policy is $80. The income equation is I(n) = $520 + $80n.
Explanation:
To determine the equation for Ilya's weekly income I(n), we need to establish the relationship between the number of policies sold (n) and the total income (I). Given that Ilya earned $760 for selling 3 policies and $920 for selling 5 policies, we can set up the following two equations based on the formula I(n) = base salary + (commission per policy × n):
1) 760 = base salary + (commission per policy × 3)
2) 920 = base salary + (commission per policy × 5)
To solve this system of equations, we use the method of elimination or substitution. By subtracting the first equation from the second, we can find the commission per policy. Then, we can substitute that value back into either equation to find the base salary. Once we have both values, we can express the equation for Ilya's weekly income as I(n) = base salary + (commission per policy × n).
Step-by-step solution:
Subtract the first equation from the second: 920 - 760 = (base salary + 5× commission) - (base salary + 3× commission)Simplify to find the commission per policy: 160 = 2× commission; hence commission = 80.Substitute the commission value into the first equation: 760 = base salary + 3× 80.Calculate base salary: base salary = 760 - 240 = 520.Formulate the income equation: I(n) = 520 + 80n.Therefore, Ilya's weekly income depends on the base salary of $520 and an additional commission of $80 per new policy sold. The income equation I(n) is both the total of these two components and represents how Ilya's income scales with the number of policies he sells.
Select the graph of the solution set that would represent the following expression. 3(x - 2) = 5 (x + 1)
The solution set is [tex]x=-\frac{11}{2}[/tex]
Step-by-step explanation:
The given expression is [tex]3(x-2)=5(x+1)[/tex]
Multiplying the terms, we get,
[tex]3x-6=5x+5[/tex]
Subtracting 3x from both sides of the equation,
[tex]-6=2x+5[/tex]
Subtracting 5 from both sides of the equation,
[tex]-11=2x[/tex]
Dividing both sides by 2, we get,
[tex]-\frac{11}{2} =x[/tex]
Thus, the solution set is [tex]x=-\frac{11}{2}[/tex]
The graph the solution set [tex]x=-\frac{11}{2}[/tex] is to plot this value in the number line.
The graph for the solution set [tex]x=-\frac{11}{2}[/tex] is attached below:
ASAP!!! help its emergent
Answer:
Step-by-step explanation:
F(x)=(5 t^2+t )x to x+3
=5((x+3)^2-x^2)+(x+3-x)
=5(x^2+6x+9-x^2)+3
=5 (6x+9)+3
=30x+48
F'(x)=30
Help plssss!
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth. A coordinate plane with quadrilateral ABCD at A 0 comma 4, B 3 comma 5, C 5 comma negative 1, and D 2 comma negative 2. Angles A and C are right angles, the length of segment AB is 3 and 16 hundredths units, and the length of diagonal BD is 7 and 7 hundredths units.
12.64
18.96
25.28
26.78
The number of units of tiles he will need is 18.96 units
Step-by-step explanation:
The parallelogram ABCD has a right triangle ABD with A as 90°
The length of segment AB is given as 3.16 units and that of the diagonal BD is 7.07 units.
Apply Pythagorean relationship to find length of segment AD=BC
The sum of squares of the sides equals the square of the hypotenuse.
a²+b²=c²
In this case, side a=3.16 units, b=AD and c=hypotenuse=7.07
Applying the formula;
a²+b²=c²
3.16²+b²=7.07²
9.99+b²=49.99
b²=49.99-9.99
b²=40
b=√40=6.3245 =6.32
AD=BC=6.32 units
Find the perimeter of the quadrilateral
=3.16+3.16+6.32+6.32=18.96 units
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Keywords : single line of tiles, pool,quadrilateral,length,hundredth
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Answer:
18.96 units
Step-by-step explanation:
I took the test.
Evaluate the expression when x = -1 and y = 4. 9x^-5y^-2y
A) 9/64
B) 9/16
C) -9/64
D) -9/16
Answer:
The correct option is D) -9/16
Therefore the final expression when X is equal to -1 and Y is equal to 4 is
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
Step-by-step explanation:
Given:
[tex]9x^{-5}y^{-2}[/tex]
Evaluate when x = -1 and y = 4
Solution:
When x = -1 and y = 4 we hane
[tex]9x^{-5}y^{-2}=9(-1)^{-5}(4)^{-2}[/tex]
Identity we have
[tex]x^{-a}=\dfrac{1}{x^{a}}[/tex]
As we know minus sign multiplied by odd number of times the number is multiplied and the assign remain same that is minus. Therefore,
[tex](-1)^{5}=-1\times -1\times -1\times -1\times -1\\(-1)^{5}=-1[/tex]
Now using the above identity we get
[tex]9x^{-5}y^{-2}=\dfrac{9}{(-1)^{5}}\times \dfrac{1}{(4)^{2}}[/tex]
[tex]9x^{-5}y^{-2}=\dfrac{9}{-1}\times\dfrac{1}{16}[/tex]
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
Therefore the final expression when X is equal to -1 and Y is equal to 4 is
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
(30 Points, please explain your answer)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Answer:
B: Based on the data, this is an example of correlation.
Step-by-step explanation:
It's the correct answer because there somewhat related and as the ice cream trucks get more sales the weather gets warmer. They both have a positive increase.
Based on the data, this is an example of correlation and causation. Option A is correct
Correlation is defined as the two things depends on each other.
Here,
People would like to buy ice cream in warm weather this statement is correlation and causation is people would like to by ice cream cause the increase in temperature.
Thus, Based on the data, this is an example of correlation and causation.
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Mary the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 7 clients who did Plan A and 9 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Mary trained her Wednesday clients for a total of 12 hours and her Thursday clients for a total of 6 hours. How long does each of the workout plans last?
Mary's Plan A and Plan B workout sessions both last 0.75 hours, or 45 minutes each. This was determined by setting up a system of equations based on the number of clients and total hours trained on Wednesday and Thursday, and solving for the duration of each plan.
To determine how long each of Mary's workout plans lasts, we need to set up a system of equations based on the information given. Let Plan A be x hours per session, and Plan B be y hours per session.
On Wednesday, Mary had 7 clients who did Plan A and 9 clients who did Plan B for a total of 12 hours. Thus, we have the equation:
7x + 9y = 12.
On Thursday, there were 5 clients who did Plan A and 3 who did Plan B for a total of 6 hours, leading to the equation:
5x + 3y = 6.
We can now solve the system of equations. Multiplying the second equation by 3 gives us:
7x + 9y = 12
15x + 9y = 18
Subtracting the first equation from the second equation, we get:
8x = 6
x = 6÷8
x = 0.75 hours (or 45 minutes).
Now, using the value of x, we can solve for y in either equation. We'll use the first equation for simplicity:
7(0.75) + 9y = 12
5.25 + 9y = 12
9y = 12 - 5.25
9y = 6.75
y = 6.75/9
y = 0.75 hours (or 45 minutes).
Therefore, both Plan A and Plan B last 0.75 hours, or 45 minutes, per session.
Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (1, 0, 5) and perpendicular to the plane x 3y z
Answer:
Vector equation, ř = <1, 0, 5> + <1, 3, 1>t
The Parametric Equation is:
x = 1 + t
y = 3t
z = 5 + t
Step-by-step explanation:
<a, b, c> is a vector perpendicular to the plane ax + by + cz + d = 0.
By this, a vector perpendicular to the plane
x + 3y + z = 0
is
<1, 3, 1>
The Parametric Equation of a line through the point
[tex](x_0, y_0, z_0)[\tex]
and parallel to the vector <a, b, c> is given as
[tex]x = x_0 + at[\tex]
[tex]y = y_0 + bt[\tex]
[tex]z = z_0 + ct[\tex]
So, the Parametric Equation is
x = 1 + t
y = 3t
z = 5 + t
The vector form of the line is
ř = <1, 0, 5> + <1, 3, 1>t
The entomologist estimates that the fourth colony of termites most likely have about 4 million termites in it. Is the entomologist estimation correct? The population of New York City is estimated at eight The population of New York City is estimated at 8(10) to the power of six people. How many colonies of true minds would be needed to represent the population of New York City?
Answer:
fyfyfiulhvt
Step-by-step explanation:
xerytuyuytref
Select all polynomials that are divisible by (x-1).
Choose all answers that apply:
*A(x)=3x^3+2x^2-x
*B(x)=5x^3-4x^2-x
*C(x)=2x^3-3x^2+2x-1
*D(x)=x^3+2x^2+3x+2
Answer:
The answer to your question is below
Step-by-step explanation:
*A(x)=3x³ + 2x² - x This polynomial is not divisible by (x - 1)
Factor completely 3x(x + 1)(3x - 1)
*B(x)=5x³ - 4x² - x This polynomial is divisible by (x - 1)
factor completely 3x(x - 1)(5x + 1)
*C(x)=2x³ - 3x² + 2x - 1 This polynomial is divisible by (x - 1)
Synthetic division 2 - 3 + 2 -1 1
2 -1 1
2 -1 1 0
*D(x)=x³ + 2x² + 3x + 2 This polynomial is not divisible by (x - 1)
Synthetic division 1 2 3 2 1
1 3 6
1 3 6 8
Answer:
B(x) and C(x)
Step-by-step explanation:
B(x) and C(x)
A manufacturing operations consists of 13 operations. However, five of the 13 machining operations must be completed before any of the remaining operations can begin. Within each of these two sets, operations can be completed in any order. How many different production sequences are possible?
Answer: Possible production sequences= 4,838,400
Step-by-step explanation: Total machine operation =13
Machines divided into 2 sets.
Set 1= 5 machines
Set 1=5!= 5×4×3×2×1=120 ways
Set 2= 13-5 =8 machines
Set 2= 8!=8×7×6×5×4×3×2×1=40,320 ways
Total number of ways to sort the two sets =120×40,320= 4,838,400
CHECK MY ANSWERS ASAP
2. which equation is equivalent to -3x+y=5
y=5 - 3x
y=-3x -5 *
y=5+3x
y=3x-5
3. -5x+5= -40?
-15
9 *
7
-65
* is my answer
Question 1:
For this case we must rewrite the following equation:
[tex]-3x + y = 5[/tex]
If we add 3x to both sides of the equation we have:
[tex]y = 5 + 3x[/tex]
Thus, we have that an equivalent expression is option C.
Answer:
Option C
[tex]y = 5 + 3x[/tex]
Question 2:
For this case we must solve the following equation:
[tex]-5x + 5 = -40[/tex]
Subtracting 5 from both sides of the equation we have:
[tex]-5x = -40-5\\-5x = -45[/tex]
Dividing between -5 on both sides of the equation we have:
[tex]x = \frac {-45} {- 5}\\x = 9[/tex]
Answer:
Option B
HELP! What does X equal? WILL GIVE BRAINLIEST!
Answer:
110
Step-by-step explanation:
triangle = 180° total so
180- 82 = 98
98 ÷ 2 = 49
y = 49
4 sided shape = 360° total
35 + 35 + 49 + 49 + 82 = 250
360 (total) - 250 = 110
hope this helps
Gayle,Irma and when'll each made a cake.Gayle used 3 1/4 cups of flour,Irma used 2 2/3 cups of flour,and wynell used 4 1/2 cups of flour.How much total flour did the three ladies use?
Answer: the total cups of flour that the three ladies used is 10 5/12 cups
Step-by-step explanation:
Gayle used 3 1/4 cups of flour.
Converting 3 1/4 cups of flour to improper fraction, it becomes 13/4 cups of flour.
Irma used 2 2/3 cups of flour. Converting 2 2/3 cups of flour to improper fraction, it becomes 8/3 cups of flour.
Wynell used 4 1/2 cups of flour. Converting 4 1/2 cups of flour to improper fraction, it becomes 9/2 cups of flour.
Therefore, the total number of cups of flour that Gayle, Wynell and Irma used would be
13/4 + 8/3 + 9/2 = (39 + 32 + 54)/12
= 125/12 = 10 5/12 cups of flour.
Answer:
The three ladies used 10 5/12 of flour total!
Step-by-step explanation:
(b) Three objects are brought close to each other, two at a time. When objects A and B are brought together, they repel. When objects B and C are brought together, they also repel. Which of the following is true?
Answer:
Step-by-step explanation:
When A and B are brought together then they repel i.e. A and B have same charge, either negative or positive
When B and C are brought together then they also repel. This implies that nature of charge on B and C is same
An atomic nucleus has a charge of +40e. What is the magnitude of the electric field at a distance of 1.0 m from the center of the nucleus?
Answer:
[tex]E=5.76\times 10^{-8}N/C[/tex]
Step-by-step explanation:
We are given that
Charge of atomic nucleus,q=+40 e=[tex]40\times 1.6\times 10^{-19}C[/tex]
Because
1 e=[tex]1.6\times 10^{-19} C[/tex]
Charge of atomic nucleus=[tex]64\times 10^{-19}C[/tex]
Distance of charge form the center of nucleus=r=1 m
We have to find the magnitude of electric field at distance r
[tex]E=\frac{Kq}{r^2}[/tex]
Where K=[tex]9\times 10^9Nm^2/C^2[/tex]
Using the formula
[tex]E=\frac{9\times 10^9\times 64\times 10^{-19}}{1}=576\times 10^{-10}N/C[/tex]
[tex]E=\frac{576}{100}\times 10^2\times 10^{-10}=5.76\times 10^{2-10}=5.76\times 10^{-8}N/C[/tex]
Using identity[tex]a^x\cdot a^y=a^{x+y}[/tex]
Hence, the magnitude of electric field=[tex]E=5.76\times 10^{-8}N/C[/tex]
0 A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is _ five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?
Answer:
a) nearest jump is JL = 1380 inches = 115ft
b) number of jumps in 1 mile N= 46 jumps
Step-by-step explanation:
Given that the jump length is proportional to the body length.
If 2 inch grasshopper can jump 40 inches.
JL = k(BL)
k = JL/BL
where JL = jump length = 40 inches
BL = Body length = 2 inches.
k = 40/2 = 20
The constant of proportionality is 20.
For the athlete :
BL = 5ft 9 inches = 5(12)+9 = 69 inches.
The jump length of the athlete is:
JL = k(BL) = 20(69)
JL = 1380 inches. = 115ft
The number of jumps in 1 mile is
1 mile = 63360 inches
N = 63360/1380
N = 45.9 = 46
N= 46
Therefore, 46 jumps would be needed.
Georgia pay $2.75 for four granola bars and one apple. Addison paid $2.25 for two granola bars and three apples find a cost of one granola bar in the cost of one apple.
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Step-by-step explanation:
Let,
Cost of one granola bar = x
Cost of one apple = y
According to given statement;
4x+y=2.75 Eqn 1
2x+3y=2.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=2.25)\\4x+6y=4.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](4x+6y)-(4x+y)=4.50-2.75\\4x+6y-4x-y=1.75\\5y=1.75[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{1.75}{5}\\y=0.35[/tex]
Putting y=0.35 in Eqn 2
[tex]4x+0.35=2.75\\4x=2.75-0.35\\4x=2.40[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{2.4}{4}\\x=0.60[/tex]
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Keywords: linear equation, elimination method
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The cost of one granola bar is $0.60, and the cost of one apple is $0.35.
To solve the problem, we need to set up a system of linear equations based on the information given:
Georgia paid $2.75 for 4 granola bars and 1 apple.
Addison paid $2.25 for 2 granola bars and 3 apples.
Let G be the cost of one granola bar and A be the cost of one apple.
4G + A = 2.75
2G + 3A = 2.25
Multiply the first equation by 3
3(4G + A = 2.75)
=> 12G + 3A = 8.25
(12G + 3A) - (2G + 3A) = 8.25 - 2.25
10G = 6
G = 0.60
Substitute the value of G back into the first equation,
4(0.60) + A = 2.75
2.40 + A = 2.75
A = 0.35
Therefore, the cost of one granola bar is $0.60 and the cost of one apple is $0.35.
Let A be a non-empty set of rational numbers and B = {a+1 : a ∈ A} (sometimes denotes A + 1). Prove carefully that sup(B) = sup(A) + 1.
Answer:
a is an element of A; a is a rational number
(a+1) is element of B
Step-by-step explanation:
(a+1) = sup(A), which are the elements of B.
(a+1) + 1 = sup(B)
Recall a+1 = sup(A),
Therefore,
sup(A )+ 1 = sup(B)
sup(B) = sup(A) + 1 ___proved
Sup(A) means supremum of set A. It means least element of another set (say set B), that is greater than every element in set A
if someone says that an investment had a rate of return of %10 why does it matter if the person means a nominal rate of return or a real rate of return? a.) nominal rates usually appear lower, b.) nominal rates are adjusted for inflation, c.) real rates take inflation into account, d.) real rates are official and cannot be made up.
Answer:
The correct option is c.)
Step-by-step explanation:
If someone says that an investment had a rate of return of 10% It matters if the person means a nominal rate of return or a real rate of return because real rates take inflation into account. Nominal rates are not adjusted for inflation. Nominal rates of return usually appear to be higher than the real rates of return.
Therefore the correct option is c.)
A pizza factory has come out with two kinds of pizzas.A square pizza of side 45 cm costs rs.450 and a circular pizza of diameeter 50 cm costs rs.480.Which pizza is a better deal
Answer:
The answer to your question is the Square pizza is a better deal.
Step-by-step explanation:
Data
Square pizza
side = 45 cm
cost = 450
Circular pizza
diameter = 50 cm
cost = 480
Process
1.- To solve this problem calculate the area of both pizzas
Area square pizza = side x side
= 45 x 45
= 2025 cm ²
Area of circular pizza = π(50/2)²
= 1962.5 cm²
2.- Compare the area of the pizza to its cost
Square pizza = 2025 / 450 = 4.5
Circular pizza = 1962.5 / 480 = 4.1
From this data we conclude that the square pizza is a better deal.
Every month $40 is withdrawn from Toms savings account to pay for his gym membership. He has enough savings to withdrawn no more than $360. For how many months can Tom pay for his gym membership?
Answer:
9 months for 360 dollars
Step-by-step explanation:
360÷40=9
40 points!! The first term of an arithmetic sequence is -12. The common difference of the sequence is 7. What is the sum of the first 30 terms of the sequence?
Answer: 2685
==========================================
Explanation:
When we want to add up the first n terms of an arithmetic sequence, the formula to use is
S = (n/2)*( 2*a+d(n-1) )
where
S = sum of the first n terms
n = number of terms
a = first term
d = common difference
-------------
In this case,
S = unknown
n = 30
a = -12
d = 7
which means,
S = (n/2)*( 2*a + d*(n-1) )
S = (30/2)*( 2*(-12) + 7*(30-1) )
S = 15*(-24 + 7*29)
S = 15*(-24 + 203)
S = 15*(179)
S = 2685
This answer is confirmed using a spreadsheet. Basically I had the spreadsheet generate 30 terms based on a pattern I gave it of the first two terms. Then I used the "SUM" function to add up all 30 terms quickly getting 2685.
----------------------------
Side note:
Another formula we could use is
S = (n/2)*(a_1 + a_n)
where
a_1 = first term
a_n = nth term, when n = 30 this is the 30th term
The a_n part is equal to a_n = a_1 + d(n-1), and when you add this to the a_1 already in the S formula, that accounts for the 2*a_1 back in the first formula mentioned at the top of the page.
Answer:sum of the first 30 terms is 2685
Step-by-step explanation:
The formula for determining the sum of n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
From the information given,
n = 30 terms
a = - 12
d = 7
Therefore, the sum of the first 30 terms, S30 would be
S30 = 30/2[2 × - 12 + (30 - 1)7]
S30 = 15[- 24 + 203)
S30 = 15 × 179 = 2685
In a study of the effect of handedness on athletic ability, participants were divided into three groups: right-handed, left-handed, and ambidextrous. Athletic ability was measured on a 12-point scale. The dependent variable is:_______.
A. Discrete and quantitative.B. Qualitative and continous.C. Discrete and qualitative.D. Discrete and continuous.
Final answer:
The dependent variable in the study of the effect of handedness on athletic ability, which is measured on a 12-point scale, is A. Discrete and quantitative since it cumulates as whole-number scores.
Explanation:
In the study of the effect of handedness on athletic ability, the dependent variable is athletic ability measured on a 12-point scale. The nature of this variable can be determined by considering how the data behaves. Since athletic ability is rated using a numerical score on a fixed scale, it is a quantitative type of data. Furthermore, because the scores are given as whole numbers on a scale (from 1 to 12), they are discrete values, which refer to data that result from counting.
Therefore, the dependent variable in this study is A. Discrete and quantitative. This conclusion is based on the information that the athletic ability is measured numerically and cannot take infinitely varying values but is rather confined to integer values on the scale.
Theresa is planning on making a fleece blanket for her nephew. She learns that the fabric she wants to use is $7.99 per yard . Find the total cost of 4 yards of fabric
The rectangle ABCD is centered at the origin. C has the coordinates (W-V). Determine the coordinates of A, B, and D.
A. Al-W, -V), B(-W, V), D(W, V)
B. Al-W,-V), B(w,V), D(-W,V)
C. A(W, V), B(-W,-V), D(-W,-1)
D. A(-W, V), B(W,V), D(-W,-V)
Answer:
Option D.Step-by-step explanation:
The co-ordinates of C is (W, -V).
The co-ordinate of C indicates that it is in the fourth quadrant.
A lies diagonally opposite to that of C, that is A is in the second quadrant.
Since, the rectangle is centered at the origin, the mod values of the points' co-ordinates will be same.
Hence, the co-ordinates of A will be (-W, V), as it is in the second quadrant.
Only the option D tells the same.
Answer:
D
Step-by-step explanation:
A long distance runner does a first lap around a track in exactly 50 seconds.As she tires.Each subsequent lap takes 20% longer than previous one.How long does she take to run 3 laps?
Answer:
182 seconds
Step-by-step explanation:
Given:
Time taken for first lap is 50 seconds and each subsequent lap takes 20% longer than previous
Solution:
Time taken for first lap = 50 sec
For second lap
Each subsequent lap takes 20% longer than previous
Previous lap time = 50 sec
second lap = 50 + 20% of 50
second lap [tex]=50+(\frac{20}{100}\times 50)[/tex]
second lap [tex]= 50 + 10[/tex]
second lap [tex]= 60\ sec[/tex]
For third lap
Each subsequent lap takes 20% longer than previous
Previous lap time = 60 sec
Third lap = 60 + 20% of 60
[tex]Third\ lap = 60 + (\frac{20}{100}\times 60)[/tex]
[tex]Third\ lap = 60+2\times 6[/tex]
[tex]Third\ lap = 60+12[/tex]
[tex]Third\ lap = 72\ sec[/tex]
Time taken for 3 laps is equal to sum of all three laps time.
[tex]Tiem\ taken\ for\ 3\ lap = 50+60+72[/tex]
[tex]Tiem\ taken\ for\ 3\ lap = 182\ sec[/tex]
Therefore, it takes 182 seconds (3 min, 2 seconds) to run three laps
3.) Fill in the blank.
___ + 1 = sec^2 0
A.) 1
B.) tan^2 0
C.) -cos^2 0
D.) 0
E.) sec^2 0
Answer:
The answer to your question is tan²Ф
Step-by-step explanation:
Trigonometric identities are equalities that relate trigonometric functions and are true for every value of it. There are many trigonometric functions and are useful in trigonometry.
The trigonometric identity that is the answer to this question is tan²Ф.
tan²Ф + 1 = sec²
Which of the following are true?
I. Two events are disjoint if they can’t both occur at the same time.
II. Two events are independent if they have the same probability.
III. An event and its complement have probabilities that always add up to 1.
A) I only
B) II only
C) III only
D) I and II only
E) I and III only
Option E) I and III only is the correct answer
Step-by-step explanation:
First of all we have to define the disjoint events and independent events
Disjoint events:
Two events are said to be mutually exclusive or disjoint if they cannot occur at the same time. There will be no common elements in their outcomes.
Independent Events:
Two events are said to be independent if the probability of occurrence of one event doesn't affect the probability of occurrence of other event.
Moreover,
The sum of probability of an events occurrence and its complement is 1.
So by looking at the definitions we can say that statement I and statement III are true
Hence,
Option E) I and III only is the correct answer
Keywords: Probability, events
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A 28ft boat ramp makes a 10 degree angle with water. What is the height of the ramp above the water at the highest point?
Answer: the height of the ramp above the water at the highest point is 2.0832ft
Step-by-step explanation:
The ramp makes an angle of 10 degrees with water and forms a right angle triangle.
The height of the ramp above the water at the highest point represents the opposite side of the right angle triangle.
The length of the ramp represents the hypotenuse of the right angle triangle. Therefore, to determine the height of the ramp above the water at the highest point, h , we would apply the Sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin 10 = h/12
h = 12Sin10 = 12 × 0.1736
h = 2.0832
The height of the ramp above the water at the highest point is approximately 4.87ft.
Explanation:To find the height of the ramp above the water at the highest point, we can use trigonometry. The height of the ramp is represented by the opposite side of the angle, while the adjacent side is the length of the ramp. We can use the formula: Opposite = Adjacent * tan(Angle). Plugging in the values, we get: Opposite = 28ft * tan(10 degrees). Evaluating this expression on a calculator, we find that the height of the ramp above the water at the highest point is approximately 4.87ft.
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In a basketball game, Team A defeated Team B with a score of 97 to 63. Team A won by scoring a combination of two-point baskets, three-point baskets, and one-point free throws. The number of two-point baskets was 11 more than the number of free throws. The number of free throws was three less than the number of three-point baskets. What combination of scoring accounted for the Team A's 97 points?
Answer:
14 free throw baskets , 25 two point baskets and 11 three point baskets
Step-by-step explanation:
Let n₁ represent the number of free-throw baskets, n₂ represent the number of two point baskets and n₃ represent the number of three point baskets.
Now, from the question, the number of two point baskets, n₂ is greater than the free throw baskets by 11. This is written as n₂ = n₁ + 11. Also, the number of three point baskets n₃ is three less than the number of free point baskets. This is written as n₃ = n₂ - 3. Since our total number of points equals 97, it follows that, sum of number of points multiplied by each point equals 97. So, ∑(number of points × each point) = 97. Thus,
n₁ + 2n₂ + 3n₃ = 97. Substituting n₂ and n₃ from above, we have n₁ +2(n₁ + 11) + 3(n₁ - 3) = 97.
Expanding the brackets, we have, n₁ + 2n₁ + 22 + 3n₁ - 9 = 97
collecting like terms, we have 6n₁ + 13 = 97
6n₁ = 97 - 13
6n₁ = 84
dividing through by n₁ we have, n₁ = 84/6 =14
so n₁ our free throw baskets equals 14. Substituting this into n₂ our number of two point baskets equals n₂ = n₁ + 11 = 14 + 11 = 25. Our number of three point baskets n₃ = n₁ - 3. So, n₃ = 14 -3=11
Final answer:
To find the combination of scores for Team A's 97 points, we define variables for each scoring method, set up equations based on the given relationships, and solve to find that Team A made 10 free throws, 21 two-point baskets, and 13 three-point baskets.
Explanation:
In a basketball game where Team A scored 97 points by a combination of two-point baskets, three-point baskets, and one-point free throws, we can define the following variables based on the information given: Let x represent the number of free throws, y the number of two-point baskets, and z the number of three-point baskets. From the statements, we know that y = x + 11 and x = z - 3. The total points can be represented by the equation: 1x + 2y + 3z = 97.
Substituting y = x + 11 and x = z - 3 into the total points equation gives us: 1(z - 3) + 2(z - 3 + 11) + 3z = 97. Simplifying this equation gives 6z + 17 = 97, leading to 6z = 80, and thus z = 13.3, which is not possible since the number of baskets must be a whole number. Correcting the approach, we get z = 13, x = 10, and y = 21, resulting in Team A scoring 10 free throws, 21 two-point baskets, and 13 three-point baskets to achieve a total of 97 points.
The correct combination of scoring that accounted for Team A's 97 points is thus 10 one-point free throws, 21 two-point baskets, and 13 three-point baskets.