None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.
what is rounding ?
Rounding is a mathematical process of approximating a number to a specified degree of accuracy. It involves replacing a number with a simpler, but close value that is easier to work with or understand.
In the given question,
The question asks us to find the annual premium for a $75,000 10-year term policy for a 25-year-old male, using the table of annual life insurance premiums per $1,000 of face value.
First, we need to find the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. Looking at the table, we can see that the premium for a 10-year term policy for a 25-year-old male is $4.79 per $1,000 face value.
To find the annual premium for a $75,000 policy, we need to multiply the premium per $1,000 face value by 75. So:
Annual premium = $4.79 per $1,000 x 75 = $359.25
Rounding this answer to the nearest cent gives us:
$359.25 ≈ $359.26
Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male is $359.26.
None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.
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Module Test Form B (RM C3 M8) Second Version) mo
13) Determine whether the following statement is true or false.
The capital letter N produces the same capital letter after being rotated 180°.
O True
O False
The statement "The capital letter N produces the same capital letter after being rotated 180°" is true.
If you rotate the capital letter N 180°, it will produce the same capital letter, as it has rotational symmetry.
The letter N has a vertical line of symmetry in the center, which means that if you rotate it 180°, it will overlap perfectly with its original position, producing the same letter.
So, the statement "The capital letter N produces the same capital letter after being rotated 180°" is true.
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If f(x)= e³x, then d/dx(e³x)=? A. 3e³x B. e³x C.ex D. 9e³x
Answer:
the answer is D. 9e³x.
Step-by-step explanation:
If f(x) = e³x, then we can find its derivative using the chain rule of differentiation as follows:
d/dx(e³x) = 3e³x * d/dx(3x) = 3e³x * 3 = 9e³x
= D. 9e³x.
Answer:
A
Step-by-step explanation:
I need help!
What is the volume of the prism? Be sure to state your answer with the units included
Answer: 105m
Step-by-step explanation:
Hope this helps! :)
Carole surveyed the class for a math project. Below are the results of her survey. What type of graph is best for Carole to display her data? A. bar graph B. line graph C. histogram D. circle graph
Answer:
A
Step-by-step explanation:
it is a bar graph because it involves class interval
the amount of money an hourly employee makes, m for working h hours can be represented by the equation m = 12.80h . what is the constant of propportionality of the equation?
The constant of proportionality of the equation would be = 12.80.
What is constant of proportionality of an equation?The constant of proportionality of an equation is the figure that represents the ratio that exists between two different variables that has direct proportional relationship.
The amount of money made by an employee is directly proportional to the number of hours they worked.
That is m directly proportional to h
The equation = m = k h. where k = 12.80 = constant of proportionality.
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t1
Question 6 (2 points)
When cooking rice, the grain is 1/2 of the part to water. Write the ratio that
represents this.
Rice:Water = 2:1
Water:Ratio = 1:2
Rice:Water = 1:2
Question 7 (2 points) ✓ Saved
Answer:
1:2
Step-by-step explanation:
In July 1964, an elderly woman was mugged in Costa Mesa, California. In the vicinity of the crime a tall, bearded man sat waiting in a yellow car. Shortly after the crime was committed, a young, tall woman, wearing her blond hair in a ponytail, was seen running from the scene of the crime and getting into the car, which sped off. The police broadcast a description of the suspected muggers. Soon afterward, a couple fitting the description was arrested and convicted of the crime. Although the evidence in the case was largely circumstantial, the two people arrested were nonetheless convicted of the crime. The prosecutor based his entire case on basic probability theory, showing the unlikeness of another couple being in that area while having all the same characteristics that the elderly woman described. The following probabilities were used. Characteristic Assumed probability Drives yellow car 1 out of 12 Man over 6 feet tall 1 out of 10 Man wearing tennis shoes 1 out of 4 Man with beard 1 out of 11 Woman with blond hair 1 out of 3 Woman with hair in a ponytail 1 out of 13 Woman over 6 feet tall 1 out of 100 Compute the probability of another couple being in that area with the same characteristics. Would you use the addition or multiplication rule? Why? Are the characteristics independent or dependent? How are the computations affected by the assumption of independence or dependence? Should any court case be based solely on probabilities? Would you convict the couple who was arrested even if there were no eyewitnesses? Comment on why in today’s justice system no person can be convicted solely on the results of probabilities. In actuality, aren’t most court cases based on uncalculated probabilities?
No, any court case should not be based solely on probabilities as probability does not imply certainty.
How to solveCompute the probability of another couple being in that area with the same characteristics
CHARACTERISTIC ASSUMED PROBABILITY
Drives a yellow car 1 out of 12
Man over 6 feet tall 1 /10
Man wearing tennis shoes 1/4
Man with beard 1/11
Woman with blond hair 1/3
Woman with hair in a ponytail 1 /13
Women over 6 feet tall 1/100
We will use the multiplication rule as all the characteristics should be present in the couple.
The probability of another couple being in that area with the same characteristics is given as
P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800
The characteristics dependent on the sum of the probabilities is not equal to 1.
The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).
No, any court case should not be based solely on probabilities as probability does not imply certainty.
No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.
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Is the following parallelogram actually a rectangle?
15 m
37 m
V 114
The given parallelogram is not a rectangle.
How to find a rectangle ?One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .
The test for a right - angled triangle is the Pythagorean Theorem which is :
Side ² + Side ² = Hypotenuse ²
Using, the dimensions, check to see if there is a right triangle :
7. 2 ² + 9. 1 ² = 12 ²
134. 65 ≠ 144
There is no right angled triangle so this is a parallelogram that is not a rectangle .
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NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality part 8a^2
Answer:
(g) D, (h) A--------------------
Part (g)'At most' means less than or equal, therefore the quotient of p and q is:
p/q ≤ 6The matching choice is D.
Part (h)'At least' means more than or equal, therefore the reciprocal of w is:
1/w ≥ 9The matching choice is A.
Answer:
g) The correct option is: p/q ≤ 6
The phrase "the quotient of p and q" means p divided by q, which is expressed as p/q. The statement "the quotient of p and q is at most 6" means that the value of p/q cannot exceed 6, but it can be less than or equal to 6. Therefore, we use the less than or equal to a symbol (≤) to represent this statement.
here is an explanation of each option:
p/q = 6: This statement indicates that the quotient of p and q is exactly 6. In other words, p/q can only be equal to 6 and not less than or greater than 6.p/q ≥ 6: This statement indicates that the quotient of p and q can be equal to 6 or greater than 6. In other words, p/q can be any value that is greater than or equal to 6.p/q > 6: This statement indicates that the quotient of p and q can be greater than 6, but not equal to 6. In other words, p/q can be any value that is greater than 6.p/q ≤ 6: This statement indicates that the quotient of p and q can be equal to 6 or less than 6. In other words, p/q can be any value that is less than or equal to 6.p/q < 6: This statement indicates that the quotient of p and q can be less than 6, but not equal to 6. In other words, p/q can be any value that is less than 6.Here's how to express each statement as an inequality in terms of 8a^2:
p/q ≤ 6:
Multiplying both sides by q, we get:p ≤ 6q
Multiplying both sides by 8a^2, we get:8a^2p ≤ 48a^2q
Therefore, the inequality for p/q ≤ 6 in terms of 8a^2 is:8a^2p ≤ 48a^2q
h) The correct option is: 1/w ≤ 9
The reciprocal of a number w is 1/w. The phrase "the reciprocal of w is at least 9" means that the value of 1/w cannot be less than 9, but it can be greater than or equal to 9. Therefore, we use the less than or equal to symbol (≤) to represent this statement.
Here's an explanation of each option:
1/w ≥ 9: This statement indicates that the reciprocal of w is greater than or equal to 9. In other words, 1/w can be any value that is greater than or equal to 9.1/w < 9: This statement indicates that the reciprocal of w is less than 9. In other words, 1/w can be any value that is less than 9.1/w ≤ 9: This statement indicates that the reciprocal of w cannot be less than 9, but it can be greater than or equal to 9. In other words, 1/w can be any value that is greater than or equal to 9.1/w > 9: This statement indicates that the reciprocal of w is greater than 9. In other words, 1/w can be any value that is greater than 9.1/w = 9: This statement indicates that the reciprocal of w is exactly 9. In other words, 1/w can only be equal to 9 and not less than or greater than 9.Here's how to express each statement as an inequality in terms of 8a^2:
1/w ≤ 9:
Multiplying both sides by w, we get:1 ≤ 9w
Subtracting 1 from both sides, we get:0 ≤ 9w - 1
Multiplying both sides by 8a^2, we get:0 ≤ 72a^2w - 8a^2
Therefore, the inequality for 1/w ≤ 9 in terms of 8a^2 is:0 ≤ 72a^2w - 8a^2
Note that the inequality for 1/w ≤ 9 involves a quadratic term with respect to "w," whereas the inequality for p/q ≤ 6 only involves linear terms with respect to "p" and "q."
i need help please also need the answer.
The correct answer as a trinomial in descending degree order is -2x^2 + 6x + 4
How to solve
Here's the step-by-step solution with the figures:
(5x^2 + 10x - 5) - (7x^2 + 4x - 9)
= 5x^2 + 10x - 5 - 7x^2 - 4x + 9 (distribute the negative sign)
= (5x^2 - 7x^2) + (10x - 4x) + ( -5 + 9) (collect like terms)
= -2x^2 + 6x + 4 (simplify and arrange in descending degree order)
Therefore, the simplified expression in descending degree order is -2x^2 + 6x + 4.
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CHED V11.1 A Select Class
babilities
What is the probability that either event will occur?
15
A
12
B
18
21
P(A or B)=P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that either event will occur is 0.68
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
The Venn diagram
On the Venn diagram, we have
Total = 15 + 12 + 18 + 12 - 12 + 21
Evaluate
Total = 66
This means that
P(A) = (15 + 12)/66
P(A) = 27/66
Also, we have
P(B) = (18 + 12)/66
P(B) = 30/66
Using the formula of the OR rule of probability:
P(A or B)=P(A) + P(B) - P(A and B)
Substitute the known values in the above equation, so, we have the following representation
P(A or B) = 27/66 + 30/66 - 12/66
Evaluate
P(A or B) = 45/66
This gives
P(A or B) = 0.68
Hence, the solution is 0.68
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I need help with this question!!!
Answer:
A. m∠X = 50°, AC = 3 cm
Step-by-step explanation:
If ABC is congruent to XYZ then the corresponding angle and sides are congruent so:
∠A = ∠X
∠B = ∠Y
∠C = ∠Z
and
AB = XY
BC = YZ
AC = XZ
Because we know m∠A is 50° and ∠A and ∠X are congruent then m∠X is also 50°
And because we know XZ is equal to 3 cm and XZ and AC are congruent then AC is also 3 cm
Kevin answered 62 questions correctly on his multiple choice history final and earned a grade of 31%. How many total questions were on the final exam?
Answer:
200
Step-by-step explanation:
Turn the 31% back to a decimal = 0.31
62/ x = 0.31
multiply each side of the equation by x to cancel it out from under the fraction
62 = 0.31x
divide each side by 0.31 to have to x alone
200 = x
Check work:
62/200 = 0.31 x 100 = 31%
please i need help i literally have an hour and 45 minutes to finish this
Answer:
0.506
0.516
0.609
0.615
Step-by-step explanation:
SHARE
Express the ratio below in its simplest form.
4.5: 3 1/2
Answer:
9 : 7
Step-by-step explanation:
4.5 : 3.5 are decimals so we can multiply them both by 2 to get whole numbers. 4.5 doubled is 9 and 3.5 doubles is 7. Therefore the ratio becomes 9:7
Mary can mow Mrs. Greenway’s lawn in 45 minutes. Mary’s little brother takes twice as long to do the same lawn. How long will it take them if they each have a mower and they work together?
Answer:
30 minutes
Step-by-step explanation:
1/45 m + 1/90 m = 1
2/9 m + 1/90 m = 1
3/90 m = 1 Multiply both sides by 90/3
90/3 x 3/90 m = 1 x 90/3
m = 90/3
m = 30
Helping in the name of Jesus.
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest) 905, 940, 955, 965, 1020, 1040, 1045, 1085, 1090, 1105 Send data to calculator Suppose that one of the people moves. His rent changes from $905 to $ 1055 Answer the following (a) What happens to the mean ? decreases by It increases by s Box It stays the same . (b) What happens to the median ? It decreases by s It increases by It stays the same .
Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.
What is mean?The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.
Here,
The average rent is determined by adding up all the rents and dividing by the total number of rents.
This is known as the mean.
Given that the person's rent increased by
=>$150, $1055 - $905 = $150.
The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.
The mean would therefore rise by
=> $150/10
=> $15.
(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.
The new median would be the middle value of the revised list, which would include the new price of $1055,
if one person's rent increased from $905 to $1055.
The median would rise given that $1055 is more expensive than $1020.
Thus , it increases by.
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Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip. If Matt made $18.50, fo how long did he babysit
The number of hours Matt babysits his sister is 1 and half hours.
Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.
Let the number of half an hours Matt babysits his sister be x.
Matt made $18.50
So, equation is 5.50x+2 =18.50
5.50x=16.50
x=16.50/5.50
x= 3
Which means 1 and half hours he babysits his sister.
Therefore, the number of hours Matt babysits his sister is 1 and half hours.
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Sophia has the following data:
131213141313h
If the range is 3, which number could h be?
A. 10
B. 11
Answer:
To determine the possible values of h, we need to first understand what is meant by the range.
The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.
The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.
So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.
If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.
Therefore, the correct answer is B. 11.
9. A counting number is totally odd if all its digits are odd and their sum is odd. How many totally odd counting numbers less than 1000 are there?
We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.
What is odd counting number?It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.
For this, let us consider all the digits from 1 to 9, and their respective sums.
Digit: 1 Sum: 1 (odd)
Digit: 3 Sum: 3 (odd)
Digit: 5 Sum: 5 (odd)
Digit: 7 Sum: 7 (odd)
Digit: 9 Sum: 9 (odd)
Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.
Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.
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Select the correct answer.
These lines are perpendicular. Is this statement true or false?
y = - 2/5x + 4
y =5/2x-3
A.true
B. false
The statement "These lines are perpendicular" is true.
These lines are perpendicular. Is this statement true or false?To determine if the two lines are perpendicular, we need to check if the product of their slopes is -1. That is, if:
m1 × m2 = -1
where m1 is the slope of the first line and m2 is the slope of the second line.
The slopes of the two lines are:
m1 = -2/5
m2 = 5/2
So, m1 × m2 = (-2/5) × (5/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular. Therefore, the statement "These lines are perpendicular" is true.
The correct answer is A. true.
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Find the sum or difference.
1. -80+77 =
2. 77 + 160 =
3. -64+ (-33) =
4. 104-(-92) =
5. -105-(-122) =
6. 185-(-154) =
7. -53-(-59) =
8. -6+ (-35) =
9. 15-(-26)-(-39) =
10. -93 +191+ (-179)
Find the product or quotient.
11. 60+ 12 =
12. -194+ (-2)=
13. 88 (-2) =
14. -12 10 =
15. -10 (-11) =
16. 90+ (-6)=
17. 3 (-59) =
18. -7 (-2) =
19. 100 (0) =
20.100/0=
After answering the presented question, we may conclude that the solution of the expressions are as follows.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
the solution of the expressions are as follows -
-3237-97196173396-4152-8172-196-176-12011084-177140undefined (division by zero is undefined)To know more about expressions visit :-
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HELP MEEEEE PLEAAASSEE!!
Whoever answers right gets marked brainliest!
Answer:
[tex]m = \frac{4 - ( \sqrt[3]{ - 6} + 4)}{0 - ( - 6))} = \frac{ \sqrt[3]{6} }{6} = .303[/tex]
So the average rate of change of g(x) over -6 < x < 0 is about .303.
Calculate the length of HG. *
10
9
8
6
5
4
3
N
M
H
3
I
5
square root 15
square root 50
square root 8
square root 51
G
9 10
Using the Pythagorean theorem, we can find the length of HG:
HG² = HI² + IG²
Therefore, the length of HG is 5sqrt(3) units.
What is pythagorean theorem?The Pythagorean Theorem is a mathematical formula that states in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
What is Length?Length is a measurement of the extent of something along its longest dimension, from one end to the other. It is often expressed in units such as meters, feet, or inches.
According to the given information:
To calculate the length of HG, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two legs.
First, we can identify that triangle HGN is a right triangle, with HG being the hypotenuse. Using the Pythagorean theorem, we have:
(HG)² = (NG)² + (NH)²
We can also identify that triangle INH is also a right triangle, with IN being the hypotenuse. Using the Pythagorean theorem, we have:
(IN)² = (NH)² + (NI)²
Substituting (NH)^2 from the second equation into the first equation, we get:
(HG)² = (NG)² + (IN)² - (NI)²
Plugging in the values given in the diagram, we get:
(HG)² = 5² + 9² - 3²
(HG)² = 61
HG = √61
Therefore, the length of HG is the square root of 61.
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HELP! LOTS OF POINTS!
Answer:
D(last option)
Step-by-step explanation:
This question might be a bit confusing since a lot of questions like this one require actually visualizing the question. The man in the lighthouse isn't trying to throw the rope directly in front of him to the birds, but rather to the boat.
The angle of depression here is the angle formed from the rope and the man's line of sight. Therefore, the angle of depression is congruent to the angle's alternate interior counterpart, which is the angle of elevation formed from the boat to the water.
From there, we solve like an angle of elevation question. We have the rope length, which is the hypothenuse, but we need to find the length of the side adjacent to the angle of elevation. So, we use cosine.
We just need to plug in the values here. The measure of the angle goes right next to the trig function we are using, and in cosine, the measure of the adjacent angle goes over the measure of the hypothenuse.
Therefore, the answer is D, or the last option.
Answer:
[tex]\textsf{D)} \quad \cos \left(24^{\circ}\right)=\dfrac{x}{45}[/tex]
Step-by-step explanation:
The angle of depression is the angle between the horizontal line of sight of the man in the lighthouse, and the direct line of sight to the boat below him.
To find how far from land the boat is, we can model the scenario as a right triangle.
The angle of depression (24°) is the angle formed by the hypotenuse and the horizontal leg of the right triangle.
If the distance to throw a rope from the top of the lighthouse to the boat is 45 feet, then the hypotenuse of the triangle is 45 feet.
The distance between the boat and the land is the side adjacent to the angle, so we can find this by using the cosine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given:
θ = 24°A = xH = 45Substitute these values into the ratio to create the required equation:
[tex]\large\boxed{\cos \left(24^{\circ}\right)=\dfrac{x}{45}}[/tex]
-2
-3
1
Attempt: 1 of
Initial
height
5
A ball is thrown from an initial height of 6 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=6+44t-16r²
Find all values of t for which the ball's height is 26 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
ground
IH
seconds
DD
X
S
The values of t for which the height of the ball is of 26 feet are given as follows:
t = 0.57 s and t = 2.18 s.
How to model the situation?The quadratic function that models the height of the ball after t seconds is given as follows:
h(t) = -16t² + 44t + 6.
The height of the ball is of 26 feet when:
h(t) = 26
Hence:
-16t² + 44t + 6 = 26
16t² - 44t + 20 = 0.
The coefficients are given as follows:
a = 16, b = -44, c = 20.
Using a quadratic function calculator, the solutions to the quadratic equation are given as follows:
t = 0.57 s and t = 2.18 s.
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which statement correctly identifies the line of reflection?
the triangles are reflected across the x-axis
the triangles are reflected across the y-axis
the triangles are reflected across the line y=x
the triangles are reflected across the line y=-x
Answer:
the triangle arereflected across the line y=x
An area of land measures 735 metres by 756 metres. It is to be divided up into
square plots of equal size.
(a) What is the area of the largest squares that will fit on it?
(b) How many squares will fit on it?
a) The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.
b) The number of squares that will fit on the land is 61773.
Explain square
A square is a geometric shape with four sides of equal length and four right angles. It is a type of rectangle, but all of its sides are the same length. Squares are used in mathematics to represent and calculate areas and volumes, and they also have applications in architecture and art.
According to the given information
(a) To find the area of the largest squares that will fit on the land, we need to find the greatest common divisor (GCD) of the dimensions 735 and 756, and then square it.
To find the GCD, we can use the Euclidean algorithm:
GCD(735, 756) = GCD(735, 756 - 735) = GCD(735, 21) = GCD(21, 735 - 21 * 35) = GCD(21, 210) = GCD(21, 210 - 21 * 10) = GCD(21, 90) = GCD(21, 90 - 21 * 4) = GCD(21, 6) = GCD(6, 21 - 6 * 3) = GCD(6, 3) = 3
Therefore, the GCD of 735 and 756 is 3. The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.
(b) To find how many squares will fit on the land, we need to divide the total area of the land by the area of each square. The total area of the land is:
735 * 756 = 555960 square meters
The area of each square is 9 square meters, as we found in part (a). Therefore, the number of squares that will fit on the land is:
555960 / 9 = 61773.333...
Since we can't have a fractional number of squares, we need to round down to the nearest integer. Therefore, the number of squares that will fit on the land is 61773.
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Question 10
Find a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36.
a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
How to find the 5 degree polynomial?Let us begin by writing the polynomial factors using the supplied zeros:
Because -2 is a zero, the polynomial has a component of (x + 2).
Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).
Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).
Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.
When we add these components together, we get:
[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]
Extending on this, we get:
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
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PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
If an ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The probability is: 84.6%.
How to find the probability?In this case, we have:
Population standard deviation (σ): $1200
Sample size (n): 400
Margin of error (E): $80
The standard deviation of the sample mean can be calculated as:
σM = σ / √n = 1200 / √400 = 60
To find the probability that the sample mean is within $80 of the population mean, we need to find the z-scores for the upper and lower limits of the interval:
Lower limit: z = (mean - E - population mean) / σM = (-80) / 60 = -1.3333
Upper limit: z = (mean + E - population mean) / σM = 80 / 60 = 1.3333
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:
P(-1.3333 < Z < 1.3333) = 0.8461
Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.846 or 84.6%.
Interpretation: This means that if we take many samples of 400 railroad-car shipments of ethanol and calculate their mean tariff rates, about 84.6% of these means will be within $80 of the true mean tariff rate of all ethanol shipments. This also means that there is a sampling error of $80, which is the maximum amount by which the sample mean may differ from the population mean due to random sampling variability.
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