The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.
What is triangle?A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.
Here,
1. Let x be the length of FH. We have:
AB/EF = BD/FH
12/8 = 10/x
Cross-multiplying, we get:
12x = 80
x = 80/12
x ≈ 6.67
Therefore, FH ≈ 6.67.
2. Let y be the length of EG. We have:
AC/BD = FH/EG
15/9 = 5/y
Cross-multiplying, we get:
5y = 135
y = 135/5
y ≈ 27
Therefore, EG ≈ 27.
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Please help I’m very confused!!
Answer:
x=-2.5
Step-by-step explanation:
3 4(2.5-5) = (1/27) 2(-2.5+10)
I hohonestly don't know how to explain it
There are 370 fish in the school pond, and 296 are goldfish. What percent of the fish are goldfish? help pls
Answer:
80% of the fish in the school pond are goldfish.
Step-by-step explanation:
To find the percentage of goldfish in the pond, we need to divide the number of goldfish by the total number of fish and multiply by 100.
percent of goldfish = (number of goldfish / total number of fish) x 100%
So, in this case:
percent of goldfish = (296 / 370) x 100%
percent of goldfish = 0.8 x 100%
percent of goldfish = 80%
Find 184.1% of 93. Round to the nearest tenth.
Answer:
171.21
Step-by-step explanation:
What is the slope of the line that passes through the points (4,7) and (8,12)
*Your answer should be numerical value only, it may be in the form of
a/b, if applicable. Remember to simplify your answer.
NEED HELP ASAP
Answer:
The slope is 5/4 or 1.25
Step-by-step explanation:
You can find the slope by using the equation (y2-y1)/(x2-x1)=Slope
This time it would be (12-7)/(8-4)
Simplified it would be 5/4 or 1.25
suppose the probability of a painter selling his art at his first art show is 16.26% . if he painted 26 pieces of art, what is the probability that he sells more than 2 of them? round your answer to four decimal places.
The probability that the painter sells more than 2 pieces of art is 0.8251.
What is the probability?The probability of the painter selling his art is P(S) = 16.26/100 = 0.1626
Since the painter painted 26 pieces of art, the number of trials, n = 26.
Let X be the random variable representing the number of pieces the painter sells. We need to find the probability that he sells more than 2 of them.
P(X > 2) = P(X = 3) + P(X = 4) + ... + P(X = 26)
Using the binomial probability formula, we have
P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ⁻ˣ⁾
where ⁿCₓ = n!/x!(n - x)!
p = probability of success
q = probability of failure = 1 - p
We can substitute n, p, and q to find P(X = x) for each x, and then add them up.
[tex]P(X > 2) = P(X = 3) + P(X = 4) + ... + P(X = 26)\\P(X > 2) = 1 - P(X = 0) - P(X = 1) - P(X = 2)\\P(X > 2) = 1 - P(X < 2)\\P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\\P(X \leq 2) = 0.0047104 + 0.0379791 + 0.1321676\\P(X \leq 2) = 0.1748571\\P(X > 2) = 1 - 0.1748571\\P(X > 2) = 0.8251429[/tex]
Rounding this to four decimal places, we get: P(X > 2) ≈ 0.8251. Therefore, the probability that the painter sells more than 2 pieces of art is 0.8251.
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Tamika was out at a restaurant for dinner when the bill came. She wanted to leave a tip of 29%. What number should she multiply the cost of the meal by to find the total plus tip in one step?
The number Tamika should multiply the cost of the meal by to find the total plus tip in one step is 1.29.
Let x be the cost of meal.
Let m be the number she should multiply the cost of the meal by to find the total plus tip in one step.
Then Total amount Tamika pays(including tip) = mx.
We need to determine the value of m.
Given Tamika wanted to leave a tip of 29% of the bill amount.
Then the amount of tip [tex]= (\frac{29}{100} )x = 0.29x[/tex]
Thus, Total amount Tamika pays(including tip) = x + 0.29x = 1.29.
We found Total amount Tamika pays(including tip) = mx.
Comparing we have m = 1.29.
A bill amount is the total cost of goods or services purchased or availed of by an individual or organization. It represents the amount that the customer owes to the provider of the goods or services. A bill may include various components such as the price of the goods or services, taxes, fees, and other charges that may be applicable.
When a customer receives a bill, they typically have a certain amount of time to pay it in full. Failure to pay the bill on time may result in additional fees, penalties, or even legal action. It is important for customers to carefully review their bills to ensure that they are accurate and that they understand all of the charges included.
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2x+2y= 24
x=3y
What is the value of x+y? I WILL MARK BRAINLIEST AND GIVE 20 POINTS
Answer:
x + y = 12
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
2x + 2y =24
x = 3y
We want to find the value of x + y.
SolvingWe first need to find the values of x and y, which we will do by solving the system.
We can solve this system by substitution.
We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.
This gives us:
2(3y) + 2y = 24
Multiply.
6y + 2y = 24
Add the terms together.
8y = 24
Divide both sides by 8.
y = 3
We found the y value, now let's find the value of x.
The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.
Substitute 3 as y.
x = 3(3) = 9
The value of x is 9.
So, to find x+y, we substitute the values we found.
x + y = 3 + 9 = 12
A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much do the barista's secret-formula beans cost per pound?
Answer: $22.50
Step-by-step explanation:
Let x be the cost per pound of the secret-formula coffee beans.
The total cost of the secret-formula beans is 12x dollars.
The total cost of the other beans is 15 × 18 = 270 dollars.
The total cost of the mix is (12 + 15) × 20 = 540 dollars.
Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.
We can set up an equation based on the total cost of the mix:
12x + 270 = 540
Subtracting 270 from both sides:
12x = 270
Dividing both sides by 12:
x = 22.5
Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.
In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?
Answer: 576
Step-by-step explanation:
134+254+188= 576
a company purchased a new computer system for $28,000. one year later, the resale value of the system was $15,700. assume that the value of the computer system declines according to an exponential model. At what rate was the value of the computer system changing 4 years after it was purchased?
A. Declining at the rate of $2,767.74 per year.
B. Declining at the rate of $1,601.26 per year.
C. Declining at the rate of $3,6214.88 per year.
D. Declining at the rate of $8,803.21 per year.
E. Declining at the rate of $2,546.52 per year.
F. None of the above.
The rate at which the value of the computer system is changing 4 years after it was purchased is "Declining at the rate of $8,803.21 per year". The correct option is D.
We can use the exponential decay formula [tex]V(t) = V0 * e^{-kt}[/tex], where V(t) is the value of the computer system after t years, V0 is the initial value, and k is the decay rate.
We know that V(1) = $15,700 and V(0) = $28,000, so we can solve for k:
[tex]$15,700 = $28,000 * e^{-k*1}[/tex]
[tex]e^{-k} = 0.5607[/tex]
-k = ln(0.5607) ≈ -0.5797
k ≈ 0.5797
Therefore, the decay rate is approximately 0.5797 per year.
To find the rate of change of the value of the computer system 4 years after it was purchased, we can take the derivative of V(t) with respect to t:
dV/dt = -k * V0 * [tex]e^{-kt}[/tex]
Substituting t = 4, V0 = $28,000, and k ≈ 0.5797, we get:
dV/dt = -0.5797 * $28,000 * [tex]e^{-0.5797*4}[/tex] ≈ -$8,803.21 per year
Therefore, the value of the computer system is declining at the rate of approximately $8,803.21 per year 4 years after it was purchased.
The correct answer is (D) Declining at the rate of $8,803.21 per year.
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a patient visits a dentist. the dentist knows that 1 in 10 patients has a toothache. one patient in 23 patients has cavity. 71% of patients with cavity has a toothache. what is the probability that the patients with a toothache has a cavity?
The probability that the patients with a toothache has a cavity is 0.3073.
Probability is the extent to which an event is likely to occur.
The probability that the patient has a toothache given that they have a cavity is equal to the percentage of patients with cavities that have toothaches. So, it can be calculated as:
P(toothache | cavity) = 71% = 0.71
Also, the probability that a patient has a cavity is equal to the ratio of patients with cavities to total patients, which is given to be 1 in 23. So,
P(cavity) = 1/23 = 0.04347
The probability that the patient has a toothache can be determined from the fact that 1 in 10 patients have a toothache. So,
P(toothache) = 1/10 = 0.1
The probability that a patient has a toothache and a cavity is calculated as:
P(toothache and cavity) = P(toothache | cavity) * P(cavity) = 0.71 * 0.04347 = 0.0308
The probability that the patient has a toothache given that they have a cavity can be calculated using Bayes' theorem:
P(cavity | toothache) = P(toothache | cavity) * P(cavity) / P(toothache)= 0.71 * 0.04347 / 0.1 = 0.3073
Therefore, the probability that patients with a toothache have a cavity is 0.3073 or about 30.73%.
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A forester reported the following distribution of tree types to a local logging company. Tree Type Spruce Pine Fir Deciduous Other Percent 52% 22% 8% 10% 8% The logging company generated a random sample of 100 trees and observed the following distribution of trees in each of the categories. Tree Type Spruce Pine Fir Deciduous Other Observed Count 51 21 10 9 9 The logging company would like to use its sample to provide convincing statistical evidence that over 50 percent of the trees in the forest are spruce trees. The logging company has decided to use a chi-square goodness-of-fit test to justify its claim. Why is the chi-square goodness-of-fit test not an appropriate procedure for the logging company to use?
The chi-square goodness-of-fit test is not an appropriate procedure for the logging company to use. It is because chi-square distribution checks for overall population distribution and not an individual category.
A chi-square goodness-of-fit test would be used to show that the entire distribution of trees in the forest is different than what the forester reported, not necessarily the individual proportion representing the spruce trees.
A statistical hypothesis test called the Chi-square goodness of fit test is used to examine whether a variable is likely to come from a certain distribution or not. It is frequently used to determine if sample data is representative of the entire population. When we have counts of values for a categorical variable, we can utilise the test. This test is equivalent to the Chi-square test of Pearson. It can be used to determine whether our expectations and the observed distribution of a categorical variable differ.
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Consider the function f (x, y) = xy - 7y - 49x + 343 on the region on or above y = x^2 and on or below y = 50. Find the absolute minimum value: -7 Find the points at which the absolute minimum value is attained. List your answer sas points in the form (a, b). (0, 50) Find the absolute maximum value: 343 Find the points at which the absolute maximum value is attained. List your answers as points in the form (a, b) (0, 0).
The absolute maximum value is attained: (0, 0)
The given function is, f(x, y) = xy - 7y - 49x + 343The region is on or above y = x^2 and on or below y = 50. To find the absolute minimum and absolute maximum value of the function, f(x, y), first we will find the critical points of the function.f(x, y) = xy - 7y - 49x + 343 ⇒ ∂f/∂x = y - 49 = 0 ⇒ y = 49 ⇒ ∂f/∂y = x - 7 = 0 ⇒ x = 7Thus, the critical point is (7, 49).Next, we will check for the boundary points. The boundary of the region is y = x^2 and y = 50. The points of intersection are:x^2 = 50 ⇒ x = ±√50 (not in the region)x = ±1.58 ⇒ y = x^2 = 2.50 (not in the region)Also, x = 0 ⇒ y = 0, and x = 0 ⇒ y = 50Thus, the critical points are (7, 49) and (0, 0).f(7, 49) = 7(49) - 7(49) - 49(7) + 343 = -7f(0, 0) = 0 - 7(0) - 49(0) + 343 = 343f(0, 50) = 0 - 7(50) - 49(0) + 343 = -357f(±1.58, 2.50) = ±1.58(2.50) - 7(2.50) - 49(±1.58) + 343 = ∓36.97The absolute minimum value is -7. The points at which the absolute minimum value is attained are (7, 49) and (0, 50).The absolute maximum value is 343. The point at which the absolute maximum value is attained is (0, 0).Hence, the required points are as follows:Points at which the absolute minimum value is attained: (7, 49) and (0, 50)Points at which the absolute maximum value is attained: (0, 0)
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A poll found that 20% of adults do not work at all while on summer vacation. In a random sample of 10 adults, let x represent the number who do not work during summer vacation Complete parts a through e a. For this experiment, define the event that represents a "success." Choose the correct answer below O Adults not working during summer vacation O Adults working during summer vacation b. Explain why x is (approximately) a binomial random variable. Choose the correct answer below. O A. The experiment consists of only identical trials. O B. The experiment consists of identical trials, there are only two possible outcomes on each trial (wworks or does not work). and the trials are independent. O C. The trials are not independent O D. There are three possible outcomes on each trial c. Give the value of p for this binomial experiment. d. Find P(x 4) P(x4) (Round to four decimal places as needed.) e. Find the probability that 2 or fewer of the 10 adults do not work during summer vacation. Plxs2): (Round to four decimal places as needed)
a) For this experiment, the event that represents a "success" is: Adults not working during summer vacation. (Option a)
b) x is (approximately) a binomial random variable because the experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent. Therefore, (option B) is correct.
c) The value of p for this binomial experiment is 0.2, which is the probability of success (i.e., an adult not working during summer vacation) on a single trial.
d) P(x≥4) is approximately 0.121.
e) the probability that 2 or fewer of the 10 adults do not work during summer vacation is approximately 0.6777.
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
So with regards to the above:
a) For this experiment, the event that represents a "success" is: Adults not working during summer vacation. (Option a)
b) x is (approximately) a binomial random variable because the experiment consists of identical trials, there are only two possible outcomes on each trial (works or does not work), and the trials are independent. Therefore, (option B) is correct.
c) The value of p for this binomial experiment is 0.2, which is the probability of success (i.e., an adult not working during summer vacation) on a single trial.
d) To find P(x≥4), we need to use the binomial probability formula:
P(x≥4) = 1 - P(x<4)
P(x<4) = P(x=0) + P(x=1) + P(x=2) + P(x=3)
Using the binomial probability formula, we can calculate:
P(x=0) = (10 choose 0) * (0.2)⁰ * (0.8)¹⁰ = 0.1074
P(x=1) = (10 choose 1) * (0.2)¹ * (0.8)⁹ = 0.2684
P(x=2) = (10 choose 2) * (0.2)² * (0.8)⁸ = 0.3019
P(x=3) = (10 choose 3) * (0.2)³ * (0.8)⁷ = 0.2013
Therefore,
P(x<4) = 0.1074 + 0.2684 + 0.3019 + 0.2013 = 0.879
And,
P(x≥4) = 1 - P(x<4) = 1 - 0.879 = 0.121
Hence, P(x≥4) is approximately 0.121.
e. To find the probability that 2 or fewer of the 10 adults do not work during summer vacation, we need to calculate P(x≤2). We can use the same formula as in part (d), but only sum up the probabilities for x=0, 1, and 2.
P(x=0) = 0.1074
P(x=1) = 0.2684
P(x=2) = 0.3019
Therefore,
P(x≤2) = P(x=0) + P(x=1) + P(x=2) = 0.1074 + 0.2684 + 0.3019
= 0.6777
Hence, the probability that 2 or fewer of the 10 adults do not work during summer vacation is approximately 0.6777.
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a) Work out the value that completes the equation for the line on the graph. b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300- 250 200 150 100 50 0 2 4 6 8 10 12 14 16 Distance cycled (miles)
The value that completes the equation for the line on the graph is -200. Keira has cycled 44.8 miles if she has burned 640 calories.
What is slope?It describes how much the dependent variable (y) changes for a given change in the independent variable (x).
According to question:a) To work out the value that completes the equation for the line on the graph, we need to find the equation of the line that passes through two points on the graph. Let's choose two points on the line, for example, (8, 250) and (16, 400).
In this case, the change in y is 400 - 250 = 150, and the change in x is 16 - 8 = 8. Therefore, the slope is:
slope = 150 / 8 = 18.75
y - y1 = m(x - x1)
Let's use the point (16, 400):
y - 400 = 18.75(x - 16)
Simplifying this equation, we get:
y = 18.75x - 200
Therefore, the value that completes the equation for the line on the graph is -200.
b) To find the distance cycled if Keira has burned 640 calories, we need to use the equation of the line we found in part (a). We can set y (calories burned) equal to 640 and solve for x (distance cycled):
640 = 18.75x - 200
840 = 18.75x
x = 44.8 (rounded to 2 decimal places)
Therefore, Keira has cycled 44.8 miles (to 2 decimal places) if she has burned 640 calories.
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if you spin the spinner 11 times, what is the best prediction possible for the number of times it will land on blue?
If the spinner is fair and has an equal chance of landing on each color, then the best prediction possible for the number of times it will land on blue when spun 11 times is 2.
If the spinner is fair, then the probability of it landing on each color is equal. Since the spinner has four colors, the probability of it landing on blue is 1/4 or 0.25.
To determine the best prediction possible for the number of times it will land on blue, we can multiply the probability of it landing on blue (0.25) by the total number of spins (11):
0.25 x 11 = 2.75
However, since we cannot have a fractional number of spins, we must round to the nearest whole number. Since 2.75 is closer to 3 than to 2, we might initially think that the best prediction for the number of times it will land on blue is 3. However, since we are looking for the best prediction possible, we need to consider the probabilities of landing on other colors as well. If we predict that the spinner will land on blue 3 times, then we are predicting that it will land on each of the other colors 2 times. This means that our total prediction is:
Blue: 3
Red: 2
Green: 2
Yellow: 2
However, this prediction is not the best possible prediction because it is not possible to have the spinner land on each of the other colors exactly 2 times. This means that we need to adjust our prediction to get as close as possible to landing on each color 2 times. The best prediction possible is:Blue: 2
Red: 3
Green: 3
Yellow: 3
This prediction is the best possible because it gets as close as possible to landing on each color 2 times while still being a whole number. Therefore, the best prediction possible for the number of times the spinner will land on blue when spun 11 times is 2.
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A car moves from rest.
The graph gives information about the speed, v metres per second, of the car t seconds after it starts to move.
Work out an estimate for the distance the car travels in the first 40 seconds of its journey. Use 4 strips of equal width.
Add up the areas of all four strips to get an estimate for the distance traveled by the car in the first 40 seconds: Distance traveled = Area of strip 1 + Area of strip 2 + Area of strip 3 + Area of strip 4.
What is area?In geometry, area is the measure of the size or extent of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width or by using specific formulas for different shapes, such as the area of a rectangle, circle, or triangle. Area is an important concept in many fields, including mathematics, physics, engineering, and architecture.
by the question.
Assuming the graph shows the speed of the car in meters per second (m/s) on the y-axis and time in seconds on the x-axis, we can estimate the distance traveled by the car in the first 40 seconds by dividing the area under the graph for that time period into four equal strips and calculating the area of each strip using the trapezium rule.
To do this, we need to find the speed of the car at four different times during the first 40 seconds, which we can do by reading off the graph. Let's say we choose the times t = 0, 10, 20, and 30 seconds.
Then we can estimate the distance traveled by the car in the first 40 seconds as follows:
Calculate the area of the first strip (from t = 0 to t = 10 seconds) using the trapezium rule:
Area of strip 1 = (1/2) x (speed at t = 0 seconds + speed at t = 10 seconds) x 10 seconds
Repeat for the other three strips, using the appropriate speeds and time intervals:
Area of strip 2 = (1/2) x (speed at t = 10 seconds + speed at t = 20 seconds) x 10 seconds
Area of strip 3 = (1/2) x (speed at t = 20 seconds + speed at t = 30 seconds) x 10 seconds
Area of strip 4 = (1/2) x (speed at t = 30 seconds + speed at t = 40 seconds) x 10 seconds
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Please help it is due tomorrow
Answer: 30
Step-by-step explanation: So what you do is,
1) Add the 25 to the 8
2) Find the sum
3) Subtract 3 from the sum
4) Done!
I hope this helps!
Best,
Abigail H
8th Grade
why does a square root have a plus or minus sign attached to it.
Answer:
To indicate that we want both the positive and the negative square root of a radicand
Answer:
Because a negative number times a negative number has a positive answer
Step-by-step explanation:
Here is the region of integration of the integral ∫6 to- 6 ∫36 to x^2 ∫36-y to 0 dz dy dx. Rewrite the integral as an equivalent integral in the following orders a. dy dz dx b. dy dx dz c. dx dy dz d. dx dz dy e. dz dx dy
The given integral is ∫6 to- 6 ∫36 to x^2 ∫36-y to 0 E)dz dX dy.
This integral can be rewritten as equivalent integrals in different orders of integration. Let's rewrite the integral in the following orders: a. dy dz dx b. dy dx dz c. dx dy dz d. dx dz dy e. dz dx dya. dy dz dx:In this case, we first integrate over z and then y and finally x.
Thus, the equivalent integral is ∫6 to- 6 ∫36 to x^2 ∫36-y to 0 dz dy dx= ∫6 to- 6 ∫36 to x^2 ∫0 to 36-y dz dy dx. Hence, the integral can be rewritten as ∫6 to- 6 ∫36 to x^2 ∫0 to 36-y dz dy dx.b. dy dx dz:In this case, we first integrate over z and then x and finally y.
Thus, the equivalent integral is ∫6 to- 6 ∫36 to x^2 ∫36-y to 0 dz dy dx= ∫6 to- 6 ∫0 to 36 ∫0 to y-36 dz dx dy. Hence, the integral can be rewritten as ∫6 to- 6 ∫0 to 36 ∫0 to y-36 dz dx dy.c. dx dy dz
In this case, we first integrate over z and then y and finally x. Thus, the equivalent integral is ∫6 to- 6 ∫36 to x^2 ∫36-y to 0 dz dy dx= ∫0 to 36 ∫-√(36-y) to √(36-y) ∫-√(36-x^2) to √(36-x^2) dz dx dy.
Hence, the integral can be rewritten as ∫0 to 36 ∫-√(36-y) to √(36-y) ∫-√(36-x^2) to √(36-x^2) dz dx dy.d. dx dz dy:In this case, we first integrate over y and then z and finally x.
Thus, the equivalent integral is ∫6 to- 6 ∫36 to x^2 ∫36-y to 0 dz dy dx= ∫0 to 36 ∫-√(36-y) to √(36-y) ∫-√(36-x^2) to √(36-x^2) dy dz dx.
Hence, the integral can be rewritten as ∫0 to 36 ∫-√(36-y) to √(36-y) ∫-√(36-x^2) to √(36-x^2) dy dz dx.e. dz dx dy:
In this case, we first integrate over y and then x and finally z.
Hence Option E is correct.
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Rotate the arrowhead 90 degrees anticlockwise around (0,0)
The new position of arrowhead graph ABCD is A'B'C'D' as shown in the below graph.
Define the term graph rotation?Graph rotation refers to the process of rotating a graph, which involves changing the orientation of the edges or nodes in the graph while preserving the relationships between them.
From the given arrowhead graph as below; the points labelled are
A (-2, 2), B (0, 5), C (2, 2) and D (0, 3)
On rotating the graph through 90° anticlockwise around the origin (0, 0), the new positions of the points are:
A (-2, 2) ⇒ A' (-2, -2)
B (0, 5) ⇒ B' (-5, 0)
C (2, 2) ⇒ C' (-2, 2)
D (0, 3) ⇒ D' (-3, 0)
Therefore, the new position of arrowhead graph ABCD is A'B'C'D' as shown in the below graph.
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What is the value of tan(A) in the diagram?
a. 12/5
b. 5/12
c. 12/13
d. 5/13
a ladder leans against the side of a house. the top of the ladder 8ft is from the ground. the bottom of the ladder is from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.
The length of the ladder is c = √(x^2 + 64) ft.
The question is asking to find the length of the ladder. We can use the Pythagorean Theorem to solve this problem. Let x be the length of the ladder.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.
The Pythagorean Theorem states that a^2 + b^2 = c^2.
Therefore, x^2 + 8^2 = c^2
Solving for c: x^2 + 64 = c^2
Taking the square root of both sides: √(x^2 + 64) = c
Therefore, the length of the ladder is c = √(x^2 + 64).
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look at the picture for the question
0.64 is the probability that a student chosen at random is in the choir or the band or both.
What does a probability simple definition entail?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
60 are in choir and band, which leaves 50 (110 - 60) in choir and not band, and 180 (240 - 60) in band and not choir, and the remaining 220 (40 - 50 - 180) students don't belong to either. So
P( choir or band ) = P(choir) + P(band ) - P( choir and band )
= 50/450 + 182/450 - 60/450 = 170/450
≈ 0.38
If instead "110 of them are in choir" means 110 students are in choir and NOT in band, and "240 of them are in bad" means 240 students are in band and NOT choir, then
P( choir or band ) = 110/450 + 240/450 - 60/450
= 0.64
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Use the following function to find d(0)
d(x)=-x+-3
d(0)=
When the function d(x) = -x +(-3), then the value of d(0) is -3
In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.
In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.
To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:
d(0) = -(0) - 3
The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as
d(0) = -3
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Label the trapezoids with the given side measures:,, and Use the similar figures and the given side lengths to complete the following prompts. Enter numerical answers only. If necessary, enter decimal numbers rounded to the nearest tenth of a number. Do not enter your answer as a fraction number
1) The length of DA = 4.5 units
2) The length of CB = 8 units
3) The length of XY = 12 units
Since trapezoids ABCD and WXYZ are similar to each other, their corresponding sides are proportional.
1) Since trapezoids ABCD and WXYZ are similar, their corresponding sides AD and WZ are parallel, and their bases AB and WX are parallel. Therefore, we can use the ratios of the corresponding sides to find DA:
DA/XY = AB/WX
DA/9 = 6/12
DA = (9/12) × 6
DA = 4.5 units
2) Similarly, we can use the ratios of the corresponding sides to find CB:
CB/ZY = AB/WX
CB/12 = 6/9
CB = (12/9) × 6
CB = 8 units
3) We can use the ratios of the corresponding sides to find XY:
AB/WX = DC/ZY
6/12 = DC/XY
DC = (6/12) × XY
DC = 0.5XY
Since ABCD is an isosceles trapezoid, DC = AB = 6. Therefore,
0.5XY = 6
XY = 12 units
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The given question is incomplete, the complete question is:
Isosceles trapezoids ABCD and WXYZ are similar to each other. Label the trapezoids with the given side measures AB=6, WX=12, and, ZW=9
Use similar figures and the given side lengths to complete the following prompts. Enter numerical answers only. If necessary, enter decimal numbers rounded to the nearest tenth of a number. Do not enter your answer as a fraction number.
1. DA =
2.CB =
3.XY =
Can someone please help me out with these two problems. I’ll award brainliest!! Thank you very very much
Answer:
QUESTION 24
To estimate the intercepts, we set f(x) to zero and solve for x:
f(x) = x^3 + 2x^2 - 5x - 6 = 0
Using synthetic division, we can find that x = -2 is a zero of the function. This means that (x + 2) is a factor of f(x), and we can write:
f(x) = (x + 2)(x^2 + x - 3)
Setting each factor to zero, we find that the intercepts are:
x + 2 = 0 -> x = -2
x^2 + x - 3 = 0 -> x = (-1 ± √13)/2
To estimate the turning points, we can use the fact that the derivative of a function is zero at a turning point. The derivative of f(x) is:
f'(x) = 3x^2 + 4x - 5
Setting f'(x) to zero, we find:
3x^2 + 4x - 5 = 0 -> x = (-2 ± √19)/3
We can now use these values to sketch the graph:
The intercepts are (-2,0) and approximately (-2.3,0.0) and (0.8,-7.5).
The turning points are approximately (-1.8,-11.1) and (0.5,-6.8).
The graph starts in the third quadrant, goes through the origin in the second quadrant, has a local maximum in the first quadrant, goes through the x-axis in the fourth quadrant, has a local minimum in the third quadrant, and goes to infinity in the second and fourth quadrants.
QUESTION 26
Here is a sketch of the graph of the polynomial function y = f(x) based on the given information:
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-----------+---------------
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The graph has two x-intercepts, one around x = -3 and one around x = 2. There is also a turning point or local maximum around x = -1 and a turning point or local minimum around x = 1. The end behavior of the graph is that it approaches negative infinity as x approaches negative infinity and approaches positive infinity as x approaches positive infinity.
Answer:
To estimate the intercepts and turning points of the function f(x) = x^3 + 2x^2 - 5x - 6, we can use a table of values.
When x = 0, f(x) = -6. So the y-intercept is (0, -6).
Factoring the polynomial, we find that the zeros are x = -3, x = -1, and x = 2. Therefore, the x-intercepts are (-3, 0), (-1, 0), and (2, 0).
To find the turning points, we can look for where the slope changes sign. We can estimate that there is a local minimum at (-2.5, -13.6) and a local maximum at (1.1, -7.3).
Using this information, we can sketch the graph of f(x).
To sketch the graph of y = f(x) with the given information, we can plot the x-intercepts (-3, 0), (-1, 0), and (2, 0). We know that the function is positive on the intervals (-∞, -3), (-2, 0), and (2, 3), so we can sketch the function above the x-axis in these regions. Similarly, we know that the function is negative on the intervals (-3,-2), (0, 2), and (3,∞), so we can sketch the function below the x-axis in these regions.
We also know that the function is increasing on the intervals (-2.67, -1) and (1, 2.5), and decreasing on the intervals (-∞, -2.67), (1, 1) and (2.5,∞). Using this information, we can sketch the function as increasing in the intervals (-2.67, -1) and (1, 2.5), and decreasing in the intervals (-∞, -2.67), (1, 1), and (2.5, ∞).
Finally, we can connect the intercepts and turning points with smooth curves to obtain a sketch of the function y = f(x).
Loving the LED's btw!
find the smallest positive integer $n$ so that \[\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2}
The smallest positive integer n so that,
$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,
we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.
Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.
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help me please i have to finish this soon and im stuck on this problem
Answer:
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Your teacher prepares a large container full of colored
beads. She claims that 1/8 of the beads are red, 1/4 are
blue, and the remainder are yellow. Your class will take a
simple random sample of beads from the container to test the teacher's claim. The smallest number of beads you
can take so that the conditions for performing inference
are met is.
15
16
30
40
90
The smallest number of beads we can take so that the conditions for performing inference are met is 40.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.
According to the Question:
Given in the question,
Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.
Quadrant Frequency
1 18
2 22
3 39
4 21
The proportions are 1/8 , 1/4 and 5/8
Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.
Now,
The expected frequencies are calculated as:
E = np₁ = 15 (1/8) = 1.875
E = np₂ = 16(1/8) = 2
E = np₃ = 30(1/8) = 3.75
E = np₄ = 40(1/8) = 5
E = np₅ = 80(1/8) = 10
Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.
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