Students at a certain high school have to take an arts or technology class. A random sample of 60 students from the high school are surveyed. Each student is asked which class they take. Based on the survey results, which of the following statements are true? Select all that apply.
A There are many excellent dancers at the high school.
B About 25% of the students at the high school
take painting.
C Of every 30 students in the high school, about 11 of them take photography.
D Next year, 7 out of every 60 students at the high school will take music.
E In a group of 120 students from the high school, about 16 of the students
likely take electronics.
Answers
The correct statements from the sample are given as follows:
B About 25% of the students at the high school take painting.
D Next year, 7 out of every 60 students at the high school will take music.
E In a group of 120 students from the high school, about 16 of the students likely take electronics.
How to obtain the proportions?The proportion relative to an outcome is given by the number of desired outcomes divided by the number of total outcomes.
15 out of 60 students at the school take painting, hence the proportion is given as follows:
p = 15/60 = 0.25 = 25%.
Out of 60 students, 11 take photography, hence out of 30 students, the amount is given as follows:
30/60 x 11 = 5.5.
For electronics, out of 120 students, we have that:
120/60 x 8 = 16.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Related Questions
42. Let P(A)=0.70,P(B∣A)=0.55 , and P(B∣A C )=0.10 . Find the following probabilities: a. P(A C ) b. P(A∩B) and P(A C ∩B) c. P(B) d. P(A∣B) 43. Complete the following probability table.
Answers
Here is the probability table to be completed: A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45
42. Let P(A) = 0.70, P(B∣A) = 0.55, and P(B∣AC) = 0.10. The following probabilities are found: a. P(AC) = 0.30 b. P(A∩B) = P(B∣A) × P(A) = 0.55 × 0.70 = 0.385 P(AC∩B) = P(B∣AC) × P(AC) = 0.10 × 0.30 = 0.03 c. P(B) = P(B∣A) × P(A) + P(B∣AC) × P(AC) = 0.55 × 0.70 + 0.10 × 0.30 = 0.415 d. P(A∣B) = P(B∣A) × P(A) / P(B) = 0.55 × 0.70 / 0.415 = 0.9289 43. Here is the probability table to be completed: A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45
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Compare two functions: f(x) shown in the table below and g(x) which is described in the following way: Darya is 2 miles east of home and begins jogging east at a constant rate of 5 miles per hour. Let g(x) be her distance away from home and x be the time she has been jogging in hours.
Which of the following statements is NOT true?
f(x) is an exponential function whose base is 3.
f(x) is an exponential growth function that will keep growing larger.
g(x) is an exponential function because Darya keeps getting farther away from home.
g(x) is a linear function because Darya is jogging at a steady rate.
Answers
It is untrue to say that the exponential function f(x) has a base of 3.
What does the function's exponential mean?A mathematical function termed an exponential function has the formula f (x) = axe, where x is a variable and a constant called the base of the function, which must be greater than 0. The most often used exponential function basis is the transcendental number e, or approximately 2.71828.
What is an example of an exponential function?An exponential function has the form f(x) = bx for b > 0 and b 1. Like in any exponential expression, the base is b and the exponent is x. Bacterial growth serves as an example of an exponential function. Some bacteria grow by two per hour.
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Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
The length AB is 2.
The length A'B' is 3.
The image is smaller than the pre-image.
The scale factor is Three-halves.
The scale factor is Two-thirds.
Answers
For the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. Yet, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.
The distance formula for the coordinates is given as:
d(A, B) = |x1 - x2|
From the figure we observe that,
d(A, B) = |2 - 4|
d(A, B) = |-2|
d(A, B) = 2 units.
Hence, option A is correct.
Also, the length of A'B' is:
d(A', B') = |3 - 6| = |-3| = 3 units.
Hence, option B is correct.
The original shape is called the pre-image in a transformation (in this example, a dilation), and the transformed shape is called the image.
The third response is untrue since the picture is larger than the pre-image.
The scale factor of the images is:
2k = 3
k = 3/2.
Hence, option 4 is correct.
The last option is also false, as the scale factor is already determined.
Hence, for the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.
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The complete question is:
What is the area?
6 ft:
6 ft
10 ft
square feet
Answers
Step-by-step explanation:
6x6x10 FT = 1 sq cube foot
What is 24/32 reduced as much as possible?
Answers
Answer:
3/4
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Divide
Solution:
3/4
Create an exponential equation passing through points (1960, 179323175) and (2010, 308745538) Round (a) and (b) to 3 decimal places
Answers
The exponential function passing through the points (1960, 179323175) and (2010, 308745538) is given as follows:
y = 0.1(1.01092581)^x.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients a and b are explained as follows:
a is the initial value.b is the rate of change.The points for this problem are given as follows:
(1960, 179323175) and (2010, 308745538).
Considering that between 1960 and 2010 there is an increase of 50 in the input, the parameter b is obtained as follows:
b^50 = 308745538/179323175
b = (308745538/179323175)^(1/50)
b = 1.01092581.
Hence:
y = a(1.01092581)^x.
When x = 1960, y = 179323175, hence the parameter a is obtained as follows:
a = 179323175/[(1.01092581)^1960]
a = 0.1.
Hence the function is:
y = 0.1(1.01092581)^x.
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molly has a $2500 down payment saved for this purchase, and the dealers $1500 cash allowance will come straight off her total. How much loan does molly need?
Answers
Based on the given question, Molly needs a loan of $1,000
What is a Loan?A loan occurs when one or more people, businesses, or other entities lend money to other people, businesses, or other entities.
The recipient incurs a debt and is often responsible for both the principal amount borrowed as well as interest payments until the debt is repaid.
How to calculate the amount of loan that Molly needs?
Molly has a $2500 down payment saved for a purchase
The dealer's cash allowance is $1500, this will be deducted from her total
The amount of loan that Molly needs can be calculated by subtracting the dealer's cash allowance from Molly's down payment
Loan= Down payment-cash allowance= 2500 - 1500= 1000
Hence Moly needs a loan of $1,000
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3⋅5 1 +2 can anyone help with this I really tried my best and I've been hard working at this but I'm still stuck at it
Answers
35 1 + 2 = 17. To remember the mathematical operations in the correct order, people frequently use the abbreviation PEMDAS.
You must follow the order of operations, often known as PEMDAS, to evaluate this equation. Parentheses, exponents, multiplication and division (left to right), addition, and subtraction are all referred to as PEMDAS (from left to right).
When using PEMDAS, you would first calculate the output of the parenthesized expression—which is 3 times 5—and then add 2.
Thus, 35 1+2 reduces to:
3*5 1 + 2 = (3*5) + 2 (first calculate within the parentheses) = 15 + 2 (conduct multiplication) = 17 (perform addition)
Hence, 35 1 + 2 = 17.
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Use the clues to crack the code the number is greater than ten the value of the ones digit is ten times the value of the tenths digit Code number (5, 5, 7,
Answers
Given that there is only one digit left and the sum is more than 10, the third digit must be 7, which it is. and the pass code to open anything it is guarding is 5 5 7, which may be inputted.
To decode the code, we know that the number is more than 10 and has three digits: . Moreover, we are aware that the value of the ones digit is 10 times that of the tenths digit. The code is 5 5 7, as may be inferred from the provided hints.
Given that the code contains two 5s, the first digit must be 5. As the value of the ones digit is 10 times that of the tenths number, the second digit must likewise be 5, which is 5. The number is bigger than 10, hence the third digit must be 7, as it is the only one still present.
In order to open whatever it is guarding, the code, which is 5 5 7, may be input.
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Which expression has a value of 15 when p=12
Answers
Answer: p+3
Step-by-step explanation:
if p=12 and you need the answer to be 15, all you need to do is find 12+_= 15. Since 12+3=15 your answer would be p+3.
solve the following system of equation y=x^2-32 y=x+10
Answers
x=(17,4)^2+(−340,−80)+58y= y^2−20y+68
y=y^2−20y+68
This is the same information as you’ll use in the next question.
The equation for the period of a pendulum is given by T space equals space 2 straight pi square root of straight L over 32 end root where T is the time (in seconds) and L is the length of the pendulum (in feet).
Find the approximate amount of time of the period of a pendulum if its length is 12 feet.
Answers
The approximate amount of time period of a pendulum with a length of 12 feet is 1.85 seconds.
What is calculus?Calculus is a branch οf mathematics that deals with the study οf change and hοw things change οver time.
We can use the given equatiοn fοr the periοd οf a pendulum:
T = 2π√(L/32)
Substituting L = 12, we get:
T = 2π√(12/32)
Simplifying:
T ≈ 1.85 seconds
Hence, the approximate amount of time of the period of a pendulum with a length of 12 feet is 1.85 seconds.
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Mr Cobb says that increasing something by 10% then decreasing it by 10% will just give you the original amount. Mr Pathuis says the new amount will be bigger. Mr Drake says the new amount will be smaller. Who is right and why?
Answers
Answer:
Mr Drake is right.
Step-by-step explanation:
Because you first decreased it by 10% of the ORIGINAL value.
You then increased it by 10% of the DECREASED value.
The percentages are the same percentages, but on different base amounts.
Simple example:
$100 decreased by 10% of $100 ($10) is $90.
$90 increased by 10% of $90 ($9) is $99.
Answer:
Mr Drake Is correct
Step-by-step explanation:
When you increase something by 10%, you multiply the original value by 1.1. When you decrease it by 10%, you multiply the increased value by 0.9. So the final amount is:
original value x 1.1 x 0.9 = 0.99 x original value
Therefore, the new amount will be slightly smaller than the original amount, and Mr. Drake is correct.
I need helppp do these all plsss show workk too
1. A team of 7 construction workers worked together to build 3
sheds in 10 days. How much of a shed did each of them build?
2. The construction of an 80-meter bridge was finished in 12
weeks. How much of the bridge was built on average each
week?
3. A 4-story building is 29 feet tall. Between which two whole
numbers do the height of each story lie?
1. Josh used 3 packages of spaghetti to make dinner for 19
guests. How much did each guest have?
2. According to a recipe, 190 grams of sugar is needed to make 9
cupcakes. Between which two whole numbers does the weight
of sugar used for each cupcake lie?
3. A 2-liter pitcher of juice was poured into 8 cups. How much
juice was in each cup?
There was 5
8
of a pie left in the fridge. Daniel ate 1/4 of the leftover pie. How much of a pie did he have?
2. Olivia took out 8 glasses and poured juice from the pitcher. The
capacity of each glass is 3/10
liter. If there was enough juice for 6 glasses, how much juice was there?
3. Pam baked some cupcakes for her friends. She baked 24
cupcakes. Each cupcake is 2/15
pound. If she packed 6
cupcakes in each box, what is the weight of each box?
Answers
Answer:
number 2 is 4
Step-by-step explanation:
The graph shows the predicted population of a town, z number of years after 2020. According to the graph, which statement is true?
Answers
According to the graph, the true statement is the population will increase more each year than the previous year. The Option B is correct.
What does population increase means?in geography context, a population growth means the increase in the number of humans on Earth. In human history, the population size was relatively stable. But with innovation and industrialization, energy, food, water, and medical care became more available and reliable.
On this graph, we can observed how the population increases from 80,000 to 100,000, 120,000, 140,000, 160,000, 180,000, 200,000, 220,000. 240,000, 260,000 and 280,000 on the Y-Axis. Therefore, the statement that population will increase more each year than the previous year is true.
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Add the number that would make the expression a perfect square. Next, write an
equivalent expression in factored form. Do not put spaces in your answers.
1. X2 + 3x+
= (x+
2. X2 + 0. 6x+
= (x+
Answers
a) We need to add 2.25 to the expression to make it a perfect square and equivalent expression is (x + 1.5)^2.
b) We need to add 0.09 to the expression to make it a perfect square and equivalent expression is (x + 0.3)^2.
a) To make the expression X^2 + 3x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 3 is 1.5, and 1.5 squared is 2.25.
X^2 + 3x + 2.25 = (x + 1.5)^2
The equivalent expression in factored form is (x + 1.5)^2, which represents a perfect square trinomial.
b) Similarly, to make the expression X^2 + 0.6x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 0.6 is 0.3, and 0.3 squared is 0.09. Therefore, we need to add 0.09 to the expression to make it a perfect square:
X^2 + 0.6x + 0.09 = (x + 0.3)^2
The equivalent expression in factored form is (x + 0.3)^2, which represents a perfect square trinomial.
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The area of the triangle below is 1/16 square centimeters. What is the length of the base. Express your answer as a fraction in simplest form
Answers
The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
What does fraction mean?A fraction is a mathematical expression which represents a part of a whole. It is written as a ratio that compares two numbers, the numerator and denominator. The numerator indicates the number of parts, the denominator indicates the total number of parts that make up the whole. Fractions can be expressed as decimals, percentages, and other forms of representation.
To solve this problem, we must use the formula for area of a triangle. This formula states that the area of a triangle is equal to one-half the product of the base and the height. In this problem, the area of the triangle is given as 1/16 square centimeters. This means that the base times the height must equal 1/8.
To find the length of the base, we must isolate the base from the equation. To do this, we must divide both sides of the equation by the height. This will leave us with the equation base = 1/8/height. Since the height is unknown, we can solve for it by taking the reciprocal of the base. This will give us the equation height = 1/8/base.
Combining both equations, we can solve for the base by multiplying both sides of the equation by 1/8. This will give us the equation base = (1/8)(1/8) = 1/64. The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
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Beth’s grandma makes homemade jam every year Beth helps her grandma by covering each jar with plastic wrap before storing the jam. each jar has a diameter of 7cm and a height of 11cm this years Beths grandma made 12 jars of jam how many square centimeters of plastic wrap will Beth need to completely cover all the jars
Answers
Beth will need approximately 3365.76 [tex]cm^{2}[/tex] of plastic wrap to cover all 12 jars of jam.
What is a Circle?
A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
So now, to calculate the surface area of each jar, we need to find the area of the circular top and the area of the rectangular side.
The area of the circular top can be calculated using the formula for the area of a circle:
[tex]A=\pi r^{2}[/tex], where r is the radius of the circle.
The diameter of the jar is given as 7 cm, so the radius is half of that:
r = [tex]\frac{7}{2}[/tex] cm = 3.5 cm
Therefore, the area of the circular top is:
A_top = [tex]\pi r^2[/tex] = π[tex](3.5)^{2}[/tex] = 38.48 [tex]cm^{2}[/tex]
The area of the rectangular side can be calculated using the formula for the area of a rectangle:
A_side = base x height
The base of the rectangle is the circumference of the circular top, which can be calculated using the formula:
C = 2πr
C = 2π(3.5) = 22 cm
So the base of the rectangle is 22 cm, and the height is 11 cm, since that is the height of the jar.
Therefore, the area of the rectangular side is:
A_side = base x height = 22 cm x 11 cm = 242 [tex]cm^{2}[/tex]
To find the total surface area of each jar, we can add the area of the circular top and the area of the rectangular side:
A_total = A_top + A_side = 38.48 [tex]cm^{2}[/tex]+ 242 [tex]cm^{2}[/tex] = 280.48 [tex]cm^{2}[/tex]
For 12 jars, the total surface area of plastic wrap needed would be:
Total area = 12 x A_total = 12 x 280.48 [tex]cm^{2}[/tex] = 3365.76 [tex]cm^{2}[/tex]
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Trinagle abc is similar to triangle def. The following ratios of corresponding sides are equal. 8/10 = 16/20 = 4x+6/4x+11
Answers
The value of x is 0. This means that [tex]8/10 = 16/20 = 4x+6/4x+11[/tex], so the corresponding sides of triangles abc and def have the same ratio.
The similarity of two triangles can be determined by the ratio of their corresponding sides. In the case of triangles abc and def, the ratio of corresponding sides is [tex]8/10 = 16/20 = 4x+6/4x+11[/tex].
To calculate the value of x, we can use the first two ratios and cross-multiply. With 8/10 = 16/20, we get 8*20=16*10, which simplifies to 160=160. Therefore, the first two ratios are equal.
To calculate the value of x using the third ratio, we can use the same method. With 4x+6/4x+11, we get ([tex]4x+6)*(4x+11)=4x^2+44x+66[/tex]. This simplifies to [tex]4x^2+44x+66=4x^2+44x+66[/tex], so the third ratio is also equal.
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Complete question:
What is the value of x in the ratio 8/10 = 16/20 = 4x+6/4x+11?
Find m angle 1 and angle 2
Answers
According to the figure and using the corresponding angle theorem we have that
angle 1 = 82 degreesangle 2 = 122 degreesHow to find angle 1 and 2Corresponding angles are pairs of angles that are formed when a straight line intersects two parallel lines.
They are located on opposite sides of the transversal (the line that intersects the parallel lines) and in corresponding positions. Corresponding angles have the same degree measurement as each other.
angle 1 = 82 degrees corresponding angles are equal
angle a = 58 degrees corresponding angles are equal
angle a and angle 2 are linear pair hence angle a and angle 2 are supplementary angles
hence we have that
angle a + angle 2 = 180 degrees
58 + angle 2 = 180
angle 2 = 180 -58
angle 2 = 122 degrees
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Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?
Answers
The probability of drawing an odd number or a multiple of 3 is 1/5.
What is probability?Probability is simply the chance that something will happen.
Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome.
Analyzing events according to their probabilities is called statistics.
So, the given data set is:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
Odd multiples of 3 are 3 and 9.
Then, the probability would be:
P(E) = 2/10
P(E) = 1/5
Therefore, the probability of drawing an odd number or a multiple of 3 is 1/5.
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ivy received a bank statement reposrting the recent changes to her account. the statement showed an overall increase in the account balance of $1,692.45. during the time shown on the statement, ivy was paid twice and withdrew a total of $1,876.23 to cover all her bills and expenses. how much (x) is each of ivay's paychecks? help me please
Answers
if Ivy received two Paychecks during the time period shown on the statement, each paycheck would be $1,784.34.
To find out how much each of Ivy's paychecks is, we need to subtract the amount she withdrew from her account from the overall increase in her account balance.
So, the calculation would be:
Overall increase in account balance - Total amount withdrawn = Total amount deposited
$1,692.45 - $1,876.23 = -$183.78
This means that Ivy actually spent more than she earned during the time period shown on the statement. Therefore, we cannot determine the amount of each of her paychecks with the given information.
However, if we assume that Ivy did not have any other income or expenses during the time period, we can use the following equation:
2x - $1,876.23 = $1,692.45
where x is the amount of each paycheck.
Simplifying the equation, we get:
2x = $3,568.68
x = $1,784.34
Therefore, if Ivy received two paychecks during the time period shown on the statement, each paycheck would be $1,784.34.
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Hey can someone help me pleaseeee SOLVE WITH EXPLANATION!!! >:(
Answers
The equation for slope is
Y2-y1/x2-y1= slope
The points we have are
(1,-5)
(-3,3)
Y=3-5=-2
X= -3-1=-4
-2/-4 the negatives cancel out leaving
2/4 and you can simplify this by dividing both parts by 2
1/2 is the final answer
A test has 12 problems, and each problem is worth 5 marks. Full marks are given for a correct answer, 2 marks are given if there is no answer, and no marks are given for an incorrect answer. Some scores between 1 and 60, are impossible to get on this test. What is the sum of these impossible scores?
Answers
To make things easier, consider the residue when each integer between equation 1 and 60 is divided by 5. The remainders might be one, two, three, or four.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0 (if all answers are wrong or not attempted) (if all answers are incorrect or not attempted)
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 60 (assuming all answers are accurate) (if all answers are correct)
10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 120 (assuming all answers are accurate and attempted twice) (if all answers are correct and attempted twice)
. The impossible scores may be obtained by locating all the numbers between 1 and 60 that cannot be stated as a sum of 0, 5, or 10.
To make things easier, consider the residue when each integer between 1 and 60 is divided by 5. The remainders might be one, two, three, or four.
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need the measure of angle ABC please
Answers
Answer:
∠ ABC = 38°
Step-by-step explanation:
given AB = DB then Δ ABD is isosceles with base angles congruent, that is
∠ BDA = ∠ BAD = 71°
the sum of the 3 angles in Δ ABD = 180° , so
∠ ABC + 71° + 71° = 180°
∠ ABC + 142° = 180° ( subtract 142° from both sides )
∠ ABC = 38°
What equation is created by this ordered pair (1,1) (2,2) (3,4) (4,7) (5,12)?
Answers
The answer will be as follows after answering the supplied question It is equation worth noting that this equation is a cubic polynomial.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
The degree n Lagrange polynomial that passes through n+1 unique points (x0,y0), (x1,y1),..., (xn,yn) is given by:
[j=0 to n] L(x) [i=0 to n, ij] * yj (x - xi)/(xj - xi) (xj - xi)
We have 5 points in our situation, thus n = 4. We get the following results by plugging the provided points into the Lagrange polynomial formula:
[tex]L(x) = 1*(x-2)(x-3)(x-4)(x-5)/(-1123) + 2(x-1)(x-3)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) (2123)+ 12(x-1)(x-2)(x-3)(x-4)/(432*1)[/tex]
When we simplify this expression, we get:
[tex]L(x) = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]
As a result, the equation of the curve passing through the given locations is:
[tex]y = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]
It is worth noting that this equation is a cubic polynomial.
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w is proportional to d
when d=35 the value of w 133
work out the value of w when d=25
Answers
Accοrding tο given proportional data when d = 25, the value οf W is 95.
What is prοpοrtiοnality?Relatiοnships between the twο variables that are prοpοrtiοnal οccur when their ratiοs are equal. Anοther apprοach tο cοnsider is that in a prοpοrtiοnal relatiοnship, οne variable is cοnsistently equal tο the οther's cοnstant value. This parameter is referred tο as the "cοnstant οf prοpοrtiοnality".
Accοrding tο the given infοrmatiοn:
Using the prοpοrtiοnality relatiοn W ∝ d, we can set up the fοllοwing prοpοrtiοn:
W/d = k, where k is the cοnstant οf prοpοrtiοnality.
Tο sοlve fοr k, we can use the values given in the prοblem:
133/35 = k
Simplifying, we get:
k = 3.8
Nοw, we can use this value οf k tο find the value οf W when d = 25:
W/25 = 3.8
Simplifying, we get:
W = 95
Therefοre, accοrding tο given infοrmatiοn when d = 25, the value οf W is 95.
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Which is the smallest?
(a) -1,
(b) -1/2,
(c) 0,
(d) 3.
Answers
Answer:
A
because it is a negative number and because it is less than -1/2
Answer:
Step-by-step explanation:
the answer is -1 as negative integers become smaller as they go to the left.
no problem
You are currently at point A on a circle, and you want to get to point B on the circle. You are trying to minimize the distance walked. You can either walk into the middle of the circle and then out of the circle, or you can walk around the edge of the circle. At what minimum distance between A and B do you walk in and then out of the circle in order to minimize the distance walked? State the answer as a % of total circumference.
Answers
To minimize the distance walked, and the minimum distance is 31.8% of the total circumference of the circle.
What is the minimum distance between A and B?
If we draw a line segment from A to B, it will intersect the circle at two points, C and D. We can find the distance AC and the distance BD by using the Pythagorean theorem.
Let r be the radius of the circle, and let x be the distance we walk in and then out of the circle.
Then, we have:
AC = √(r^2 - (x/2)^2)
BD = √(r^2 - (x/2)^2)
The total distance we walk is AC + BD + AB. Since AB is fixed, we want to minimize AC + BD.
AC + BD = 2√(r^2 - (x/2)^2)
To minimize this expression, we need to maximize the value inside the square root. That means, we need to set (x/2)^2 to be as small as possible.
In other words, we want x to be as large as possible.
The maximum value of x is the diameter of the circle, which is 2r.
If we walk in and out of the circle along the diameter, then AC and BD are both equal to r, and the total distance we walk is 2r + AB.
Therefore, the percentage of the total circumference that we walk in and out of the circle is:
2r / (2πr) * 100% = 100/π ≈ 31.8%
So, we need to walk in and out of the circle at two points that are opposite to each other, along a diameter, to minimize the distance walked, and the minimum distance is approximately 31.8% of the total circumference of the circle.
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Answers
By writting all the numbers as decimals we can see that the lake that lost the least amount of water is the last one.
Which lake lost the least amount of water?The first lake lost a fraction of 5/6 of its total water.
The second lake lost the 85% of its water.
The last lake lost a fraction of 246/300 of its water.
We want to see which of these 3 numbers is the smaller one, we can write all of them as decimals ot get:
5/6 = 0.833
85% = 0.85
246/300 = 0.82
With this we conclude that the lake that lost the least amount of water is the last one.
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