Therefore, the answer is that Franklin must have bought at least 4 packs of pumpkin seeds to have an equal number of pumpkin and sunflower seeds.
What do you mean by LCM?LCM stands for Least Common Multiple. It's the lowest positive number that's a multiple of two or further given figures. In other words, it's the lowest number that all the given figures divide into unevenly.For illustration, the LCM of 2 and 3 is 6, because 6 is the lowest number that's a multiple of both 2 and 3. Another illustration, the LCM of 4, 6, and 8 is 24, because 24 is the lowest number that's a multiple of all three of those figures.LCM is a useful conception in calculation, especially when dealing with fragments, because it helps us find a common denominatorGiven by the question.
Sure! Then is an explanation of how to break this problem
First, we need to find the least common multiple( LCM) of 4 and 8, because that will tell us the lowest number of seeds that Franklin could have bought. To find the LCM, we can list the multiples of each number until we find one that they've in common
Multiples of 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 8 8, 16, 24, 32, 40, 48, 56, 64.
The first multiple that appears in both lists is 8, so the LCM of 4 and 8 is 8.
Now we know that Franklin bought the same number of pumpkin seeds and sunflower seeds, and that number is a multiple of 8. So, we just need to find the lowest multiple of 8 that's also a multiple of 4. That is 8 itself, because it's formerly a multiple of 4.
So, Franklin must have bought at least 4 pumpkin seed packs, since each pack contains 4 seeds. Any other multiple of 8 that's also a multiple of 4 would also work, but 8 is the lowest similar number.
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Compare your answer with the average density of the giant's envelope, if it has a 0.5 solar mass and its radius is 0.6 AU . Express your answer using two significant figures.
The required average density of the giant envelope is equal to 3.30 x 10^9 kg/m^3.
Average density of the giant's envelope, required the mass and volume of the envelope.
Let us assume that the giant is a sphere with a radius of 0.6 AU,
the volume of the envelope is ,
V = (4/3)πr³
= (4/3)π(0.6 AU)³
= (4/3)(3.14)(0.6 × 149.6 ×10⁶ )³
To convert this volume to units of cubic meters,
Multiply by the conversion factor by,
1 AU = 149.6 x 10⁶m
⇒1 AU³ = (149.6 x 10⁶ km)³
⇒1 AU³ = 3.35 x 10³³ m³
Now ,calculate the density of the giant's envelope using the formula,
density = mass / volume
Giant's envelope has a mass of 0.5 solar masses,
which is equivalent to,
M = 0.5 x 1.99 x 10³⁰ kg
= 9.95 x 10²⁹ kg
Average density of the giant's envelope is equals to,
⇒ density = 9.95 x 10²⁹ kg / (4/3)(3.14)(0.6 × 149.6 ×10⁶ )³
= 3.30 x 10^9 kg/m^3
Therefore, the average density of the giant's envelope is approximately 3.30 x 10^9 kg/m^3.
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Venell put together a model train with 25 train cars. Each train car is 80 millimeters long. How many meters long is Venell's model train if there are no gaps between cars? (1 meter = 1,000 millimeters)
Answer: 2 meters
Step-by-step explanation:
The length of one train car is 80 millimeters. Therefore, the length of the entire train is:
25 cars × 80 mm per car = 2000 mm
To convert millimeters to meters, we need to divide by 1000:
2000 mm ÷ 1000 = 2 meters
Therefore, Venell's model train is 2 meters long.
A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.
x 0 1 2 3 4 5 6
p(x) 0.10 0.15 0.20 0.25 0.20 0.05 0.05
Calculate the probability of each of the following events.
(a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}
(e) {between two and four lines, inclusive, are not in use}
(f) {at least four lines are not in use}
The probability of each of the events of {at most three lines are in use}, {fewer than three lines are in use}, {at least three lines are in use, {between two and five lines, inclusive, are in use}, {between two and four lines, inclusive, are not in use} and {at least four lines are not in use} are 0.70, 0.45, 0.55, 0.80, 0.35 and 0.40 respectively.
The problem involves finding probabilities of different events for a mail-order company with six telephone lines. The probability mass function (pmf) is given, and we use it to calculate the probabilities of different events such as "at most three lines are in use" or "between two and five lines, inclusive, are in use".
To calculate these probabilities, we use basic probability formulas such as the addition rule, subtraction rule, and the complement rule.
P(X ≤ 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70
P(X < 3) = 0.10 + 0.15 + 0.20 = 0.45
P(X ≥ 3) = 1 - P(X < 3) = 1 - (0.10 + 0.15 + 0.20) = 0.55
P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X < 2) = (0.10 + 0.15 + 0.20 + 0.25 + 0.20) - 0.10 = 0.80
P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.20 = 0.65, so P(2 ≤ X ≤ 4)ᶜ = 1 - 0.65 = 0.35
P(X ≥ 4) = 0.20 + 0.05 + 0.05 = 0.30, so P(X ≤ 3) = 1 - P(X ≥ 4) = 0.70 - 0.30 = 0.40
These formulas are applied based on the given events to determine the probabilities.
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Complete the proof of the identity by choosing the Rule that justifies each step.
To see a detailed description of a Rule, select the More Information Button to the right of the Rule.
Statement Rule 1. Algebra
cosx/sinx (sec*2x - 1) Rule ? 2. Quotient
cosx/sinx (tan*2x) Rule ? 3. Pythagorean
cosx/sinx (sin*2x/cos*2x) Rule ? 4. Odd/Even
sinx/cosx Rule ? 5. Reciprocal
tanx Rule ?
Find the rules answers towards each statement
All rules towards each statement shown in table below.
Define the term trigonometry?The relationships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It entails the study of trigonometric functions like sine, cosine, and tangent, which connect a triangle's angles and side lengths.
Rules towards each statement:
Statements
Rule1. Cos x/ Sin x (Sec 2x - 1) Pythagorean identity
Rule2. Cos x/Sin x (Tan 2x) Algebra
Rule3. Cos x/Sin x (Sin 2x/Cos 2x) Reciprocal
Rule4. Sin x/Cos x Odd/ Even
Rule5. Tan x Quotient
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As per trigonometric functions, rules towards each statement are:
Rules towards each statement:
Statements
Rule1. Cos x/ Sin x (Sec 2x - 1) Pythagorean identity
Rule2. Cos x/Sin x (Tan 2x) Algebra
Rule3. Cos x/Sin x (Sin 2x/Cos 2x) Reciprocal
Rule4. Sin x/Cos x Odd/ Even
Rule5. Tan x Quotient
What exactly does trigonometry mean?Trigonometry is a branch of mathematics that focuses on the relationships between triangles' sides and angles. It requires studying the trigonometric functions that link the angles and side lengths of a triangle, such as sine, cosine, and tangent.
Rules towards each statement:
Statements
Rule1. Cos x/ Sin x (Sec 2x - 1) Pythagorean identity
Rule2. Cos x/Sin x (Tan 2x) Algebra
Rule3. Cos x/Sin x (Sin 2x/Cos 2x) Reciprocal
Rule4. Sin x/Cos x Odd/ Even
Rule5. Tan x Quotient
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A bag is filled with an equal number of red, yellow, green, blue, and purple socks. The theoretical probability of a child drawing 2 yellow socks from the bag with replacement is one fifth. If the experiment is repeated 175 times, what is a reasonable prediction of the number of times he will select 2 yellow socks?
one fifth
10
25
35
35 is a reasonable prediction of the number of times he will select 2 yellow socks?
what is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
What is event?In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.
In the given question,
The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:
P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25
So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.
To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:
E(X) = n * p
where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.
In this case, n = 175 and p = 1/25. So,
E(X) = 175 * (1/25) = 7
Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.
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The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
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What is the length of arc HI?
picture below
solve the equation
x/2-2=4+1/2
Step-by-step explanation:
7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd
In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?
The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.
An employee who earned $20,000 will contribute $260 to the welfare fund.
To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.
The first $1000 will have a contribution rate of 4%.
Contribution for the first $1000 = 4% of $1000 = $40.
The next $1000 will have a contribution rate of 3%.
Contribution for the next $1000 = 3% of $1000 = $30.
The next $1000 will have a contribution rate of 2%.
Contribution for the next $1000 = 2% of $1000 = $20.
The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.
Contribution for the remaining amount = 1% of $17,000 = $170.
Now, let's sum up the contributions for each tier:
$40 + $30 + $20 + $170 = $260.
Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.
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Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
Convert 555 into base five numberal system
The decimal number 555 is written as 4210 in base-5.
Answer: [tex]555_{10} =4210_{5}[/tex]
Step-by-step explanation:
Decimal to base five conversion
we divide the decimal number by 5 repeatedly until the quotient becomes 0here
We apply the rule to convert 555 into base five numeral.Divide the number 555 repeatedly by 5 until quotient becomes zero.D Q Remainders
5 |555 0
5 |111 1
5 |22 2
5 |4 4
0
here , Divisor = 5 , Quotient = [555,111,22,4,0] , Remainders = [4210]Can you help me to solve these two questions?
The equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.
What do a curve's tangent and normal lines represent?A line that meets a curve at a point and has the same slope as the curve there is said to be the tangent line to that curve. A line that is perpendicular to the tangent line at a given position is the normal line to a curve at that location. In other words, the normal line's slope equals the tangent line's slope's negative reciprocal. The normal line is helpful for determining the direction of greatest change of the curve at a place whereas the tangent line gives information about the instantaneous rate of change of the curve at that point.
The given function is f(x) = 1/x.
The slope of the function is the derivative of the function thus,
f(x) = 1/x
f'(x) = -1/x²
f'(7) = -1/49
The equation of the line is given as:
y - y1 = m(x - x1)
where, m is the slope of the equation.
The equation of the tangent line is:
y - f(7) = f'(7)(x - 7)
y - 1/7 = -1/49(x - 7)
y = (-1/49)x + 8/49
b. The equation of the normal line to the graph is given as:
The slope of the normal line is negative and opposite of the tangent line.
That is,
m = 49.
y - f(7) = 49(x - 7)
y - 1/7 = 49(x - 7)
y = 49x - 342
Hence, the equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.
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Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Rolling a six-sided die 80 times and recording the number of l's rolled, Answer Tables Yes AN No There are more than two possible outcomes on each trial of the experiment. The experiment does not consist of n identical trials. The trials are dependent
Rolling a six-sided die 80 times and recording the number of l's rolled and it is a Binomial Distribution.
The binomial distribution is a probability distribution used in statistics that summarizes the probability that a value will take on one of two independent values given a set of parameters or assumptions. The binomial distribution is calculated by multiplying the probability of success by the power of the number of successes and by multiplying the probability of failure by the power of the difference between the number of successes and the number of trials. The product is then multiplied by the combination of trials and successes.
For example, suppose a casino develops a new game where participants bet on the number of heads or tails in a specified number of coin tosses. Suppose a contestant wants to bet $10 that 20 coin tosses will result in exactly 6 heads. The participants wanted to calculate the probability of this happening, so they used calculations from the binomial distribution.
The probability is calculated as :
(20! / (6! × (20 - 6)!)) × (0.50)⁶ × (1 - 0.50)⁽²⁰⁻⁶⁾. Therefore, the probability of getting exactly 6 heads out of 20 coin tosses is 0.037, or 3.7%.
In this case, the expected value is 10 heads, so the contestant made a bad bet.
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Three dice are rolled. What is the probability of getting the sum as 13?
When three dices are rolled.
Total number of outcomes = = 216
Sum of 13 can be achieved in the following ways:
From the digits 6,4,3
So, there are 3! ways = = 6
From the digits 6,2,5
So, there are 3! ways = = 6
From the digits 5,4,4
So, there are ways = 3
From the digits 6,6,1
So, there are ways = 3
From the digits 3,5,5
So, there are ways = 3
So, total numbers whose sum is 13=
So, Probability = .
Therefore, the probability of getting sum as 21 on rolling three dice = .
5. Which of the graphs below illustrates water boiling in Denver, Colorado?
Your question is incomplete. The complete question is: Which of the graphs below illustrates water boiling in Denver, Colorado? (Altitude 1,600 meters.)
Answer:
The graphs that come with this question are in the picture attached.The answer is graph identified with the letter A.Explanation:
The normal boiling point of water is 100°C. That is the temperature at which water boils when the atmospheric pressure is 1 atm, i.e. at sea level.
The liquids boil when its vapor pressure equals the atmospheric pressure; so the higher the atmospheric pressure the higher the boiling point, and the lower the atmospheric pressure the lower the boiling point.
Since, it is stated that the altitude of Denver, Colorado is 1,600 m, the atmospheric pressure (the pressure exerted by the column of air above the place) is lower than 1 atm (atmospheric pressure at sea level).
Hence, water boiling point in Denver is lower than 100°C.
The graphs shown represent the temperature (T °C) as water is heated. Since when liquids boil their temperature remains constant during all the phase change, the flat portion of the graph represents the time during which the substance is boiling.
In the graph A, the flat portion is below 100°C; in the graph B, the flat portion is at 100 °C; in the graph C the flat part is above 100ªC, and, in graph D, there is not flat part. Then, the only graph that can illustrate water boiling in Denver, Colorado is the graph A.
Please answer these questions correctly :)
Find the percent of each number :-
1.) 64% of 75 tiles :
[tex] \implies \sf \: \dfrac{64}{100} \times 75 \\ \\\implies \sf \:0.64 \times 75 \\ \\ \implies \sf \: 48 \\ [/tex]
Hence, 64% of 75 tiles is 48 tiles.
2.) 20% of 70 plants.
[tex] \implies \sf \: \dfrac{20}{100} \times 70 \\ \\\implies \sf \:0.2 \times 70 \\ \\ \implies \sf \: 14 \\ [/tex]
Hence, 20% of 70 plants is 14 plants.
3.) 32% of 25 pages .
[tex] \implies \sf \: \dfrac{32}{100} \times 25 \\ \\\implies \sf \: 0.32 \times 25 \\ \\ \implies \sf \: 8 \\ [/tex]
Hence, 32% of 25 pages is 8 pages.
4.) 85% of 40 e -mails.
[tex] \implies \sf \: \dfrac{85}{100} \times 40 \\ \\\implies \sf \:0.85 \times 40 \\ \\ \implies \sf \: 34 \\ [/tex]
Hence, 85% of 40 e -mails is 34 e-mails.
5.) 72% of 350 friends.
[tex] \implies \sf \: \dfrac{72}{100} \times 350 \\ \\\implies \sf \:0.72 \times 350 \\ \\ \implies \sf \: 252 \\ [/tex]
Hence, 72% of 350 friends is 252 friends.
6.) 5% of 220 files.
[tex] \implies \sf \: \dfrac{5}{100} \times 220 \\ \\\implies \sf \:0.05 \times 220 \\ \\ \implies \sf \: 11 \\ [/tex]
Hence, 5% of 220 files is 11 files.
A regular hexagon is inscribed into a circle. Find the length of the side of the hexagon, if the radius of the circle is 12 cm.
A. 20 cm
B. 18 cm
C. 16 cm
D. 12 cm
E. None of these
Answer:
D, 12 cm.
Step-by-step explanation:
First, draw out the circle with a hexagon in it. I did this by dividing the circle into thirds and then halving each of those because it was easier to visualize. I ended up with something like the image below. Now, we know that the sum of all of the angles that come together at the center of the circle is going to be 360. We can divide 360 by 6 to get 60. The top angle of the triangle, the angle closest to the center, is 60 degrees. We also know that the length of all of these legs that are going out will be the same, because the radius of the circle is constant. This makes each triangle an isosceles triangle. Given the isosceles base angle theorem, both base angles of the triangle must be the same. The sum of all angles in a triangle is 180 degrees. So the equation for x, one of the angles, would be 60 (angle closest to center) + 2x = 180. Let's subtract 60 from both sides to get 2x = 120. Divide both sides by two to get x = 60. Okay, so now we know that all angles in the triangle are 60 degrees. By the equilateral triangle theorem, we know these triangles must be equilateral because all of their angles are 60 degrees. Equilateral triangles also have the same side lengths. Because 12 is one side length, then all side lengths = 12. Therefore, the length of one side of the hexagon is 12.
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polygon trig is a quadrilateral. which of the following pieces of information would prove that trig is a parallelogram?
The pieces of information would prove that the polygon trig is a parallelogram is GI || TR (option b).
Now, suppose you have a quadrilateral named TRIG. The question asks which of the given information would prove that TRIG is a parallelogram. Let's examine each option to determine which one satisfies the conditions of a parallelogram.
a) GT || IR: This option tells us that GT is parallel to IR. However, we cannot conclude that TRIG is a parallelogram from this information alone.
b) GI || TR: This option states that GI is parallel to TR. Again, we cannot immediately conclude that TRIG is a parallelogram from this information.
c) GO ≅ OR, TO ≅ OI: This option tells us that GO is congruent to OR and TO is congruent to OI. However, this information alone does not prove that TRIG is a parallelogram.
d) GR ≅ TI: This option states that GR is congruent to TI. Similarly, we cannot conclude that TRIG is a parallelogram from this information.
e) GO ⊥ OI: This option tells us that GO is perpendicular to OI. Unfortunately, this information alone does not prove that TRIG is a parallelogram either.
f) GT ≅ TR: This option states that GT is congruent to TR. However, this information alone does not prove that TRIG is a parallelogram.
The answer is option (b) GI || TR. If GI is parallel to TR, then by definition, TRIG has opposite sides parallel, which means it is a parallelogram.
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Complete Question:
Polygon TRIG is a quadrilateral.
Which of the following pieces of information would prove that TRIG is a parallelogram?
a) GT || IR
b) GI || TR
c) GO ≅ OR, TO ≅ OI
d) GR ≅ TI
e) GO ⊥ OI
f) GT ≅ TR
In a particular class of 24 students, 16 are men. What fraction of the students in the class are women?
The fraction of the students in the class are women is one-third (1/3)
How to calculate he fraction of the students in the class are womenIf there are 16 men in the class of 24 students, we can find the number of women by subtracting the number of men from the total number of students:
Number of women = Total number of students - Number of men
Number of women = 24 - 16
Number of women = 8
Therefore, there are 8 women in the class.
To find the fraction of students in the class who are women, we divide the number of women by the total number of students:
Fraction of students who are women = Number of women / Total number of students
Fraction of students who are women = 8 / 24
Fraction of students who are women = 1/3
So, one-third (1/3) of the students in the class are women.
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What triangles are similar to triangle ABC?
Answer:
A right angled triangle is similar to triangle ABC
Step-by-step explanation:
If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°
And if a triangle has one angle of 90° then it is a right angled triangle
Hope you understand :)
Evaluate (can't write decimal answer).
[tex]sin(20)sin(70)-sin(14)cos(26)-cos(6)cos(84)[/tex]
The evaluation of sin(20)sin(70) - sin(14)cos(26) - cos(6)cos(84) is approximately -1.
How to solve trigonometry?Use the trigonometric identities to simplify the expression:
sin(20)sin(70) - sin(14)cos(26) - cos(6)cos(84)
= (sin(20)cos(20)) / 2 - (sin(14)sin(64)) / 2 - (cos(6)cos(6)) / 2
= [(sin(40) - sin(80)) / 2] - [(cos(50) - cos(78)) / 2] - [(1 + cos(12)) / 2]
= (sin(40) - cos(50) + cos(78) - sin(80) - 1 - cos(12)) / 2
Now, use a calculator to evaluate each trigonometric function:
sin(40) = 0.6428, cos(50) = 0.6428, cos(78) = 0.2079, sin(80) = 0.9848, cos(12) = 0.9781
Substituting these values:
= (0.6428 - 0.6428 + 0.2079 - 0.9848 - 1 - 0.9781) / 2
= -2.755 / 2
= -1.3775
Therefore, the value of the given expression is approximately -1.
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[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25} } } )[/tex]
find the value of y ~
The simplification of the given expression
[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]
is y = 7
How to simplify expressions?[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]
find the square root of 25
[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]
simplify root 9 - 5
[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]
find the square root of 4
[tex]y = ( \sqrt{47 + 2)} [/tex]
Add root 47 and 2
[tex]y = ( \sqrt{49} )[/tex]
Find the square root of 49
y = 7
Therefore, the solution to the given expression is y = 7
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A sample of 245 high school students from grades 9-10 and 11-12 were asked to choose the kind of band to have play at a school dance
Let's break down this question. How many students were in each grade? In grades 9-10, there were 122 students, and in grades 11-12, there were 123 students. What kind of bands were the students asked to choose from? Were they given a list of bands to choose from, or were they simply asked to suggest a band they would like to see?
Given f(x) = x³ + kx + 9, and the remainder when f(x) is divided by x − 2 is 7,
then what is the value of k?
Answer:
k = -5
Step-by-step explanation:
According to the Remainder Theorem, when we divide a polynomial f(x) by (x − c), the remainder is f(c).
Therefore, if we divide polynomial f(x) = x³ + kx + 9 by (x - 2) and the remainder is 7 then:
f(2) = 7To find the value of k, simply substitute x = 2 into the function, equate it to 7 and solve for k.
[tex]\begin{aligned}f(2)=(2)^3 + k(2) + 9 &= 7\\8+2k+9&=7\\2k+17&=7\\2k&=-10\\k&=-5\end{aligned}[/tex]
Therefore, the value of k is -5.
convert 49% to a fraction
Answer:
To convert 49% to a fraction, we can simply write it as 49/100. This is because a percentage is a way of expressing a number as a fraction of 100. So 49% means 49 out of 100, which can be written as the fraction 49/100.
Answer:
49/100
Step-by-step explanation:
Percent means out of 100.
49%
49/100
if cos is the 4 quadrant
The exact value of sin∅ if cos∅ =3/8 and in the fourth quadrant is 292⁰
What are the angles in the 4th quadrant?We should recall that the the angles of the 4th quadrant range from 270° to 360°. that is to say that in the fourth quadrant, 270≤x≤360
The given angle is cos∅ =3/8
cos∅ = 0.375
Find the angle we take the cos inverse
That ∅ = Cos⁻¹0.375
∅ = 68⁰
In the fourth quadrant, cos is positive that 360-68 = 292⁰
Then the exact value of sin is 292⁰
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Find the 16th term of the arithmetic sequence described below.
ak = 3 + 4 (k − 1)
Show your work here
Answer: 63
Step-by-step explanation:
The given arithmetic sequence is defined by the formula:
ak = 3 + 4(k - 1)
To find the 16th term, we can substitute k = 16 into this formula and simplify:
a16 = 3 + 4(16 - 1)
a16 = 3 + 4(15)
a16 = 3 + 60
a16 = 63
Therefore, the 16th term of the arithmetic sequence is 63.
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
92 19 41 24 75 53 70 3 67 64 9
Step-by-step explanation:
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = Largest value - Smallest value
Range = 92 - 3
Range = 89
To find the variance and standard deviation, we need to calculate the mean first:
Mean = (Sum of all values) / (Number of values)
Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11
Mean = 45.09 (rounded to two decimal places)
Next, we need to calculate the variance:
Variance = (Sum of squared differences from the mean) / (Number of values - 1)
Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)
Variance = 1071.45 (rounded to two decimal places)
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = Square root of variance
Standard deviation = Square root of 1071.45
Standard deviation = 32.74 (rounded to two decimal places)
The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.
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I have two fair dice each numbered 1 to 6. I am going to throw the two dice. What is
the probability that the sum of the numbers on the dice will be a square number?
The probability that the sum of the numbers on the dice will be a square number is 1/6.
What is the mathematical probability?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
We can first make a list of every conceivable result when rolling two dice in order to determine the likelihood that the sum of the numbers on the two dice will be a square number:
[tex](1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6[/tex])
[tex](2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)[/tex]
[tex](4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)[/tex]
[tex](6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]
The sums can then be listed, and the square numbers can be identified:
2, 3, 4, 5, 6, 7
3, 4, 5, 6, 7, 8
4, 5, 6, 7, 8, 9
5, 6, 7, 8, 9, 10
6, 7, 8, 9, 10, 11
7, 8, 9, 10, 11, 12
The likelihood that the sum of the numbers on the dice will be a square number is 6 out of a total of 36 potential outcomes.
P(square sum) = 6/36 = 1/6.
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Consider the function h(x) = a(−2x + 1)^5 − b, where a does not=0 and b does not=0 are constants.
A. Find h′(x) and h"(x).
B. Show that h is monotonic (that is, that either h always increases or remains constant or h always decreases or remains constant).
C. Show that the x-coordinate(s) of the location(s) of the critical points are independent of a and b.
Answer:
A. To find the derivative of h(x), we can use the chain rule:
h(x) = a(-2x + 1)^5 - b
h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4
To find the second derivative, we can again use the chain rule:
h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3
B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.
C. To find the critical points, we need to find where h'(x) = 0:
h'(x) = -10a(-2x + 1)^4 = 0
-2x + 1 = 0
x = 1/2
Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.