Answer: Without a perpendicular cut, we cannot determine the height of the triangle directly. However, we can use the Pythagorean Theorem to find it indirectly.
Let's assume that Francine has cut the paper into a right triangle ABC, where AB and BC are the legs of the triangle, and AC is the hypotenuse. Let x be the length of AB and y be the length of BC. We can then use the Pythagorean Theorem to find the length of AC:
AC^2 = AB^2 + BC^2
We don't know the exact values of AB and BC, but we do know that the area of the triangle is given by:
Area = (1/2) * AB * BC
We can use this formula to find the area in terms of x and y:
Area = (1/2) * x * y
Now we need to eliminate one of the variables (either x or y) so that we can express the area in terms of the other variable and AC. We can do this by rearranging the Pythagorean Theorem to solve for one of the variables:
x^2 = AC^2 - y^2
y^2 = AC^2 - x^2
Let's solve for y:
y^2 = AC^2 - x^2
y = sqrt(AC^2 - x^2)
Now we can substitute this expression for y into the formula for the area:
Area = (1/2) * x * sqrt(AC^2 - x^2)
To find the maximum possible area, we need to maximize this expression. We can do this using calculus, by taking the derivative of the expression with respect to x, setting it equal to zero, and solving for x. However, since we only need an approximate answer to the nearest tenth of a square centimeter, we can use trial and error to find the value of x that gives the maximum area. We can start by trying different values of x, and using a calculator to evaluate the expression and find the corresponding area.
Let's try a few values of x:
If x = 0, then the area is 0.
If x = AC/2 (i.e., if the triangle is isosceles), then the area is (1/8) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.
If x = AC/sqrt(3) (i.e., if the triangle is equilateral), then the area is (1/4) * AC^2 * sqrt(3), which is approximately 0.433 * AC^2.
Since the area is maximized when the triangle is equilateral, we can assume that the piece of paper is an equilateral triangle, and use the formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) * side^2
where side is the length of one of the sides of the triangle. To find the side length, we need to know the length of AC. We don't know the exact value of AC, but we can estimate it by measuring the length of the longest side of the piece of paper (assuming that it is the hypotenuse of the triangle). Let's say that the longest side is 30 cm. Then, by the Pythagorean Theorem, we can find the length of the other two sides:
x^2 + y^2 = 30^2
x^2 + (sqrt(AC^2 - x^2))^2 = 30^2
2x^2 + AC^2 - x^2 = 900
x^2 = (900 - AC^2)/
Step-by-step explanation:
The Zyco corporation pays an annual dividend of $2.10 per share. on Tuesdays it closed at $72 per share with a net change of +0.95. The dividend remained at $2.10 for several months. What was the yield on Tuesday? Round to the nearest tenth of a percent. At what price did Zyco close on Monday? nWhat was thenyield at Monday's Close? Round to the nearest tent of a percent?
In response to the given question, we have that Therefore, on Tuesday, equation the yield was 2.92%, and on Monday, it was 2.96%.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.
Divide the yearly dividend by the share price to determine the yield, then multiply the result by 100 to get the percentage:
Tuesday's yield is calculated as (Annual dividend / Share Price) times 100.
Tuesday's yield is calculated as ($2.10 / $72) times 100, which is 2.92%.
Tuesday's closing price minus Monday's closing price is the difference.
The price on Monday was $72 minus $0.95.
$71.05 was the final price on Monday.
We apply the same procedure as previously to determine the yield as of Monday's close:
Monday's yield is calculated as (annual dividend / share price) x 100.
Yield on Monday is equal to ($2.10 / $71.05) times 100, or 2.96%.
Therefore, on Tuesday, the yield was 2.92%, and on Monday, it was 2.96%.
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The volume of the right cone below is 1152\piπ units^3
3
. Find the value of x.
x
12
The volume of the right cone below is 1152π/3 cubic units then the value of x is 24.
What is the volume of a right circular cone?The volume of a right circular cone is given by the formula:
V = (1/3)πr²h
where π is pi (approximately equal to 3.14), r is the radius of the circular base, and h is the height of the cone.
In this problem, we are given that the volume of the cone is 1152π/3 cubic units and that the value of x is related to the radius and height of the cone.
Let's first write the formula for the volume of the cone in terms of x:
V = (1/3)π(x/3)²(x/3)
Simplifying this expression, we get:
V = (1/27)πx²
We are given that V = 1152π/3, so we can substitute this into the formula above and solve for x:
1152π/3 = (1/27)πx³
Multiplying both sides by 27/π, we get:
x³ = 1152*27/3
x³ = 27648
Taking the cube root of both sides, we get:
x = 24
Therefore, the value of x is 24.
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Anne wants to make a scale drawing of her house with the drawing showing a ratio 1 inch to 12 feet.
If Anne's house is 84 feet long, how long, in inches, should her scale drawing be?
7 in
[tex] \frac{1}{2} = \frac{x}{84} \\ 84 \times \frac{1}{12} = \frac{x}{84} \times 84 \\ 84 \times \ \frac{1}{12} = x \\ 7 = x[/tex]
What is a frequency table? Explain what is meant by the categories and frequencies. What is meant by relative frequency? What is meant by cumulative frequency?
_______________________________________
A. Categories are descriptions of data, such as ages of people living in a city or the annual salaries of professional athletes. They always represent counts or measurements. The frequency of a category is the number of data values in the category.
B. Categories are descriptions of data, such as which brand names of shoes sold in a store or audience ratings of films. They always describe qualities. The frequency of a category is the number of data values in the category.
C. Frequencies are descriptions of data, such as which grades students received on a test or the heights of trees in a forest. They can describe qualities or represent counts or measurements. The category of a frequency is the number of data values in the frequency.
D. Categories are descriptions of data, such as which grades students received on a test or the heights of trees in a forest. They can describe qualities or represent counts or measurements. The frequency of a category is the number of data values in the category.
* I tried option C its was not it so... ._., Help!? Ty :)
The correct options for the frequency table problem is -
D. Categories are descriptions of data, such as which grades students received on a test or the heights of trees in a forest. They can describe qualities or represent counts or measurements. The frequency of a category is the number of data values in the category.
What is frequency table?
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.
D. Categories are descriptions of data, such as which grades students received on a test or the heights of trees in a forest.
They can describe qualities or represent counts or measurements.
The frequency of a category is the number of data values in the category.
A frequency table is a table that displays the categories or groups of a set of data along with their corresponding frequencies.
The categories are typically represented in the left column, and the frequencies are listed in the right column.
The categories represent the possible values or ranges of values that the data can take.
For example, in a frequency table of student grades on a test, the categories might be "A," "B," "C," "D," and "F."
The frequency of a category is the number of times that the data falls within that category.
For example, if there are 20 students in a class and 5 of them received an "A" on a test, then the frequency of the "A" category would be 5.
Relative frequency is the proportion or percentage of observations in a category relative to the total number of observations.
It is calculated by dividing the frequency of a category by the total number of observations.
For example, if there are 20 students in a class and 5 of them received an "A" on a test, then the relative frequency of the "A" category would be 5/20 = 0.25 or 25%.
Cumulative frequency is the running total of frequencies for a set of data.
For example, if the frequency of the "A" category is 5 and the frequency of the "B" category is 10, then the cumulative frequency of the "B" category would be 5 + 10 = 15.
It represents the total number of observations that fall within a category and all previous categories.
Therefore, the correct option is D.
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What is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x) +
9?
shifted up
shifted left
shifted down
shifted right
Answer would be shifted up
Step-by-step explanation:
hence the +9 you would be going up 9 units :)
what is the value of p
Answer:
52 - 13 = 39 so p = 39
Step-by-step explanation:
Answer:
P=25
Step-by-step explanation:
180=52+90+p+30
180=155+P
180-155=p
p=25
please helpppppp!!!!!!!!!!!
The percent of the fluid ounces under 60 is option D. Not here
How do you calculate the percent of the fluid ounces?To calculate the percentage of fluid ounces, you first need to determine the total volume of the container in fluid ounces. Then, you need to determine the volume of the specific substance that you are interested in as a fraction of the total volume. Finally, you can convert this fraction into a percentage by multiplying it by 100.
Here's the formula to calculate the percentage of fluid ounces:
Percentage of fluid ounces = (Volume of substance in fluid ounces ÷ Total volume of container in fluid ounces) x 100%
For example, if you have a 16 fluid ounce container of juice and you want to know what percentage of the container is filled with orange juice, and you measure that there are 4 fluid ounces of orange juice, you can calculate the percentage of orange juice as follows:
Percentage of orange juice = (4 fluid ounces ÷ 16 fluid ounces) x 100% = 25%
Therefore, the orange juice fills 25% of the 16 fluid ounce container. It could then be concluded that the percent of the fluid ounces is not here.
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Describe the sampling distribution of p^ Assume the size of the population is 15,000 n = 700, P = 0.172 determine the standard deviation of the sampling distribution of p^
Answer
The shape of sampling distribution of ^p is approximately normal because n < greater than 0.05N and np (1-p) > less than 10.
Step-by-step explanation:
The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
What is defined by the Central Limit Theorem?The distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n is defined by the central limit theorem, where:
The mean is [tex]\mu[/tex] = 9.The standard deviation is √p (1-p)/ n The shape is approximately normal.As long as these two conditions are respected:
n≤ N
np(1-p) > 10.
Here, we have the parameters
n= 700, p = 0.172, N= 15, 000
So, n/N = 0.0466 < 0.05
and, np(1-p)
= 700 x 0.172 ( 1- 0.172)
= 99.69 >10
Then the shape is approximately normal.
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Mrs. Smith has gallon of orange juice. She divides it equally
among her 8 grandchildren. How much orange juice does each
grandchild get?
Which equation models the situation?
7(x+8)=49
i know the answer but tell me how did you solve it only with numbers and mathematical letters nothing else
What are the values of x when x²+x-6 = -4?
OA. x = -4 and x = 6
OB. x = -2 and x = 1
OC. x = -3 and x = 2
OD. x = -5 and x = -6
edu
play
Answer:
0
Step-by-step explanation:
for x x^2+x-6=-4. x2+x−6=−4 x 2 + x - 6 = - 4. Step 1. Add 4 4 to both sides of the equation. x2+x−6+4=0 x 2 + x - 6 + 4 = 0.
(hope it helps!)
Question
Let C be the event that a randomly chosen cancer patient has received chemotherapy. Let E be the event that a randomly
chosen cancer patient has received elective surgery. Identify the answer which expresses the following with correct
notation: Of all the cancer patients that have received chemotherapy, the probability that a randomly chosen cancer patient
has had elective surgery.
Answer:
The probability that a randomly chosen cancer patient who has received chemotherapy has also had elective surgery can be expressed as P(E|C), where "P" represents probability and the vertical bar "|" indicates "given." So, P(E|C) represents the probability of event E given that event C has occurred.
Step-by-step explanation:
Please can someone go in detail with the answer, I will give the brainliest!
Two Italians and three Englishmen are looking for accommodation in the hotel as loyal guests. In the hotel for accommodation their loyal guests are guarded by 8 rooms, of which 3 rooms have walls painted blue, in 3 rooms in green color, and in the remaining 2 rooms in yellow color. Italians want to be either in blue or in the yellow room, and the English in either the green or the yellow room. In how many ways did the two Italians and three Englishmen can be assigned rooms so that each of them is alone in one room?
Answer:
To solve this problem, we can use the principle of inclusion-exclusion. We first count the total number of ways to assign rooms to the Italians and Englishmen without any restrictions. Then, we subtract the number of ways that violate the Italian's restriction, and the number of ways that violate the Englishmen's restriction. Finally, we add back the number of ways that violate both restrictions.
Step 1: Total number of ways to assign rooms
There are 8 rooms, so there are 8 choices for the first person, 7 choices for the second person, and so on. Therefore, there are 8 x 7 x 6 x 5 x 4 = 6,720 total ways to assign rooms to the Italians and Englishmen without any restrictions.
Step 2: Number of ways that violate the Italian's restriction
There are 3 blue rooms and 2 yellow rooms, so there are 3 x 2 = 6 ways to assign rooms to the Italians that violate their restriction. For each of these ways, there are 6 x 5 x 4 = 120 ways to assign rooms to the Englishmen. Therefore, there are 6 x 120 = 720 ways that violate the Italian's restriction.
Step 3: Number of ways that violate the Englishmen's restriction
There are 3 green rooms and 2 yellow rooms, so there are 3 x 2 = 6 ways to assign rooms to the Englishmen that violate their restriction. For each of these ways, there are 5 x 4 x 3 x 2 = 120 ways to assign rooms to the Italians. Therefore, there are 6 x 120 = 720 ways that violate the Englishmen's restriction.
Step 4: Number of ways that violate both restrictions
If the Italians are in blue rooms and the Englishmen are in yellow rooms, there is only 1 choice for this assignment. If the Italians are in yellow rooms and the Englishmen are in green rooms, there are also only 1 choice for this assignment. Therefore, there are 2 ways that violate both restrictions.
Step 5: Calculate the final answer
Using the principle of inclusion-exclusion, we can calculate the number of ways that satisfy all the restrictions as follows:
Total number of ways - Number of ways that violate the Italian's restriction - Number of ways that violate the Englishmen's restriction + Number of ways that violate both restrictions
6,720 - 720 - 720 + 2 = 5,282
Therefore, there are 5,282 ways to assign rooms to the two Italians and three Englishmen so that each of them is alone in one room, while satisfying their loyal guest preferences.
Step-by-step explanation:
learner sell 300 vetkoet every week for 12 they charge 10 for each vetkoet calculate the profit they will if the cost for each vetkoet is 3.80
The profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To calculate the profit for selling 300 vetkoek every week, we need to first calculate the total revenue generated and the total cost of producing the vetkoek.
Total revenue = Price per vetkoek x Number of vetkoek sold
Total revenue = 10 x 300 = 3000
Total cost = Cost per vetkoek x Number of vetkoek sold
Total cost = 3.80 x 300 = 1140
Profit = Total revenue - Total cost
Profit = 3000 - 1140 = 1860
Therefore, the profit for selling 300 vetkoek every week at a cost of 3.80 per vetkoek and selling them for 10 each is 1860.
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The sum of an odd integer and 4 times the next consecutive integer is 63
Find the value of the greater integer
Answer:
the greater integer is "y", which is 13.
Step-by-step explanation:
Let's call the odd integer "x", and the next consecutive integer "y". Since "y" is the next consecutive integer after "x", we know that:
y = x + 2
We are told that the sum of "x" and 4 times "y" is 63. We can set up an equation to represent this:
x + 4y = 63
Now we can substitute the expression for "y" in terms of "x" into this equation:
x + 4(x + 2) = 63
Simplifying this equation, we get:
x + 4x + 8 = 63
5x + 8 = 63
Subtracting 8 from both sides, we get:
5x = 55
Dividing both sides by 5, we get:
x = 11
So the odd integer is 11. We can use the expression for "y" in terms of "x" to find the next consecutive integer:
y = x + 2 = 11 + 2 = 13
Therefore, the greater integer is "y", which is 13.
Answer:
13
Step-by-step explanation:
there is an interval of 2 between consecutive odd numbers
let n and n + 2 be the 2 consecutive integers , then
n + 4(n + 2) = 63 , that is
n + 4n + 8 = 63
5n + 8 = 63 ( subtract 8 from both sides )
5n = 55 ( divide both sides by 5 )
n = 11
then larger integer is n + 2 = 11 + 2 = 13
If you spin the spinner 88 times,
what is the best prediction possible
for the number of times it will land on
green?
The answer is 6
but specifically, it can land on green 6.8181%
what's the end behavior of: y= 2 + log2(x - 1)
We can infer that the function y = 2 + log2(x - 1) has the following final behaviour:
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.what is a function?A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input. Y = f is a common way to represent a function (x).
A function in mathematics is a certain configuration of the inputs (also known as the domain) and their outputs (also known as the codomain), where each input has precisely one output and the output can be connected to its input.
from the question;
We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behaviour of the function
y = 2 + log2(x - 1).
The formulas (x - 1) and log2(x - 1) also approach infinity as x gets closer to positive infinity. As a result, y increases as x moves closer to positive infinity. The following can be written:
lim x→∞ 2 + log2(x - 1) = ∞
Expression (x - 1) moves closer to zero and log2(x - 1) moves closer to negative infinity as x moves towards 1 from the right. So, as x moves closer to 1 from the right, y moves closer to negative infinity. The following can be written:
lim x→1+ 2 + log2(x - 1) = -∞
This leads us to the following conclusion about the final behaviour of the function y = 2 + log2(x - 1):
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.to know more about the function visit:
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For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 4 minutes of play, one half the game awards 1/2 point, and for every 12 minutes of play, one and one half the game awards 1 1/2 points. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many points are awarded for 20 minutes of play? (2 points)
Answer:
Step-by-step explanation:
Therefore, 12 minutes of play awards 4.5 points.
The constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that for every 4 minutes of play, 1/2 point is awarded.
For every 12 minutes of play, 1 1/2 points are awarded.
We can set up a proportion to find the constant of proportionality:
(1/2 point) / (4 minutes) = (3/2 points) / (12 minutes)
Simplifying the left side, we get:
1/8 = (3/2 points) / (12 minutes)
Multiplying both sides by 12, we get:
1.5 = (3/2)P
P = (1.5) x (2/3) = 1
Therefore, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded.
By constant of proportionality, the equation that represents the relationship between the number of points awarded and the amount of time played:
P = (1/4)t
To find the number of points awarded for 20 minutes of play, we can use the equation P = (1/4)t:
P = (1/4)(20)
= 5
Hence, the constant of proportionality is 1/4, which means that for every minute of play, 1/4 point is awarded and 5 points are awarded for 20 minutes of play.
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What is the quotient of 16sup(x,-2)-8sup(x,-2)-2sup(x,-9) and 2x?
The required quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.
What is arithmetic?Arithmetic involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Here,
To simplify the given expression, we can start by factoring out the common factor of 2x from the numerator. This gives:
(16x⁻² - 8x⁻² - 2x⁻⁹) / 2x
Next, we can simplify the terms in the numerator by combining the like terms:
= (4x⁻² - x⁻⁹) / x
= 4x⁻²⁻¹ - x⁻⁹⁻¹
= 4x⁻³ - x⁻¹⁰
= 4x⁻³ - x⁻¹⁰
Therefore, the quotient of the expression 16x⁻² - 8x⁻² - 2x⁻² divided by 2x is 4x⁻³ - x⁻¹⁰.
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help me pls i will give brainless
Find measurement of side A'C' and B'C'?
Answer:
AC = 14.9
BC = 10.5
Step-by-step explanation:
The triangle is a isosceles right triangle with ∠B = 90o, ∠A = ∠C = 45o.
Therefore AB = BC = 10.5
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse, which is AC.
AC^2 = AB^2 + BC^2
AC^2 = 2AB^2
AC^2 = 2(10.5)^2
AC^2 = 220.5
AC = √220.5 = 14.85 or 14.9
. Aisha went to the local gas station to get a gallon of milk. She saw that the store had quart containers of milk for $1.19 while a gallon was $4.66. Aisha bought four quarts instead of the gallon because she thought it would be cheaper for the same amount of milk. Did Aisha save money? Explain your reasoning.
Therefore , the solution of the given problem of unitary method comes out to be she actually paid more for the same quantity of milk in the end.
What does unitary method mean?Divide the measures of just this microsecond portion by two variable in order to complete the task using the unitary technique. Briefly stated, the characterised by a group and colour subgroups are both removed from the unit method expression when a wanted item is present. For example, 40 pens with a changeable price would cost Rupees ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this.
Here,
4 gallons of milk make up a gallon of milk. Four pints would cost $1.19 each, or
=> $1.19 x 4 = $4.76.
Instead of purchasing a gallon of milk for $4.66,
Aisha opted to purchase four pints for $4.76.
Thus, by purchasing four pints rather than a gallon, Aisha did not save money.
She actually paid more for the same quantity of milk in the end.
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2x(x+4) in standard form
Answer:
To write 2x(x+4) in standard form, we need to expand the product and simplify:
2x(x+4) = 2x^2 + 8x
Therefore, the standard form of 2x(x+4) is 2x^2 + 8x.
Step-by-step explanation:
100 POINTS PLEASE HELP
Consider the surface
Find the following partial derivatives
The value of dz/ dt using Chain Rule is (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex].
What is Chain Rule?The chain rule states that the derivative D of a composite function is given by a product, as D(f(g(x))) = Df(g(x)) ∙ Dg(x).
In other words, the first factor on the right, Df(g(x)), indicates that the derivative of f(x) is first found as usual, and then x, wherever it occurs, is replaced by the function g(x).
Given:
By chain rule we can write z= f(x, y) = f( x(t), y(t))
dz/ dt = df/ dx . dx/ dt + df/ dy. dy/dt
So, df/ dx = [tex]e^y[/tex]
df/dy = [tex]e^y[/tex] + (x+ y) [tex]e^y[/tex]
x(t)=5t, while y(t)=1-t², So,
So, dx/dt = 5
and, dy/dt = -2t
Now, dz/ dt = 5 . [tex]e^y[/tex] + -2t ( [tex]e^y[/tex] + (x+ y) [tex]e^y[/tex])
= (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex]
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find the area of this semi circle with radius r=19cm give your answer rounded to 1 dp
the answer is 283.4
I can't write a formula
Select the equation that represents this problem: Anthony read 5 /6 hour each day for 2 days. A. 2 × 5 6 = 10 12 B. 2 × 5 6 = 10 × 1 6 C. 2 + 5 6 = 2 5 6 D. 5 1 + 5 1 + 5 1 + 5 1 + 5 1 + 5 1 = 30 6
you will get brainless
An equation that represents this problem "Anthony read 5/6 hour each day for 2 days." is: A. 2 × 5/6 = 10/12.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we can reasonably infer and logically deduce that Anthony's reading rate is 5/6 hour on a daily basis and for a period of 2 days only:
Total number of hours = 2 × 5/6
Total number of hours = 10/12 hours.
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Every morning before your first class, you line up at Tim Horton's on the BCIT campus.
You notice that it takes between 19 to 35 minutes to get through the lineup, give your
order to the cashier, and receive your coffee, donut, and wrap. The time to get your
order follows a uniform distribution.
(a) What is the probability that it will take at least 23minutes to get your order??
(enter a number between 0 and 1 in 4 decimal places)
(b) You arrive at Tim Horton's at 7:30am. What is the probability that you receive your
order before your friends show up at 8:00am at Tim's?
(enter a number between 0 and 1 in 4 decimal places)
(c) 10% of the time it takes you longer than how many minutes to get your
order?
(answer in 2 decimal places)
min
Answer: (a) Since the time to get the order follows a uniform distribution between 19 to 35 minutes, the probability of getting the order in any interval of time within this range is proportional to the length of that interval. Therefore, the probability of taking at least 23 minutes to get the order is:
P(X ≥ 23) = (35 - 23) / (35 - 19) = 0.4
Rounding to 4 decimal places, the probability is:
P(X ≥ 23) ≈ 0.4000
(b) If you arrive at Tim Horton's at 7:30am and your friends show up at 8:00am, you have 30 minutes to receive your order. Since the time to get the order follows a uniform distribution, the probability of receiving the order before your friends show up is the probability of getting the order in 30 minutes or less, which is:
P(X ≤ 30) = (30 - 19) / (35 - 19) = 0.5789
Rounding to 4 decimal places, the probability is:
P(X ≤ 30) ≈ 0.5789
(c) Let's call the time in minutes to get the order that is longer than 10% of the time as t. Since the distribution is uniform, we know that the probability of taking longer than t minutes is 0.1. Therefore, we can write:
(35 - t) / (35 - 19) = 0.1
Solving for t, we get:
t = 19 + 0.9(35 - 19) = 32.4
Rounding to 2 decimal places, we get:
t ≈ 32.40 minutes
Therefore, 10% of the time it takes longer than 32.40 minutes to get the order.
Step-by-step explanation:
The population of Mexico between 1921 and 2010 can be modeled as
p(t) = 8.028e^0.025t million people, where t is the number of years since 1900.†
(a) What was the population of Mexico in 2006? (Round your answer to three decimal places.)
____________ million people
How rapidly was the population of Mexico growing in 2006? (Round your answer to three decimal places.)
____________ million people per year
(b) Write a linearization of p in 2006. (Round all numerical values to three decimal places.)
pL(t) = ______________
(c) Use linearization to estimate the population of Mexico in 2011. (Round your answer to three decimal places.)
_______________ million people
By answering the above question, we may state that As a result, in 2006, equation Mexico's population was expanding at a pace of around 2.708 million people each year.
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
We must enter t = 2006 - 1900 = 106 into the population model and do the following calculations to get the population of Mexico in 2006:
p(106) = 8.028e (0.025 * 106) million individuals
108.191 million individuals, or p(106) (rounded to three decimal places)
Finding the derivative of the population model with respect to time t will allow us to determine how quickly Mexico's population was rising in 2006:
Each year, p'(t) = 0.025 * 8.028e(0.025t) million individuals.
We may then calculate the derivative at time t = 106 as follows:
P'(106) = 0.025 * 8.028e(0.025*106) million individuals annually P'(106) 2.708 million individuals annually (rounded to three decimal places)
As a result, in 2006, Mexico's population was expanding at a pace of around 2.708 million people each year.
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squared root of x-45 equals squared root of x minus 3
Answer:
No solution
Step-by-step explanation:
[tex]\sqrt{x-45} =\sqrt{x-3} \\(\sqrt{x-45} )^2=(\sqrt{x-3} )^2\\x-45 = x-3\\x-x = 45-3\\0 = 42\\[/tex]
PLEASE HELP !! ASAP :)
Based on the given information, the graph of the function will shift 6 units up from the parent graph, f(x).
What is function?A function is a mathematical rule that relates one input value to one output value. The parent graph of a function is the simplest form of the graph that shows the basic behavior of the function.
In this case, the function is being shifted vertically by 6 units. This means that all points on the graph will be shifted upward by 6 units compared to the parent graph.
The shape of the graph will remain the same, but its position will change. Understanding how functions are transformed is important in mathematics and can be used to model a wide range of real-world phenomena.
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