Answer:
\(l \approx 15.455\,ft\)
Step-by-step explanation:
The length of the ramp is computed with the help of the following trigonometric function:
\(\sin \theta = \frac{h}{l}\)
\(l = \frac{h}{\sin \theta}\)
\(l = \frac{4\,ft}{\sin 15^{\circ}}\)
\(l \approx 15.455\,ft\)
The perimeter of a rectangle is 56 feet. What are the dimensions of the rectangle with maximum area?
Answer:
A rectangle is a 2-dimensional geometrical shape formed by four perpendicular sides. Out of four sides, two sides are unique, and the other two sides are similar to the unique sides. These two unique sides are the dimensions of a rectangle.
Step-by-step explanation:
A rectangle is a 2-dimensional geometrical shape formed by four perpendicular sides. Out of four sides, two sides are unique, and the other two sides are similar to the unique sides. These two unique sides are the dimensions of a rectangle.
if the sum of three real numbers is $0$ and their product is $17$, then what is the sum of their cubes?
Answer:
51
Step-by-step explanation:
x + y + z = 0 →- -(x + y) = z → z^3 = - (x^3 + 3x^2y + 3xy^2 + y^3)
xyz = 17
xy [ -(x + y) ] = 17
xy (x + y) = -17 → x^2y + xy^2 = -17 → 3x^2y + 3xy^2 = -51
So......
x^3 + y^3 + [ z^3 ]
x^3 + y^3 + [ - ( x^3 + 3x^2y + 3xy^2 + y^3) ] =
-3x^2y - 3xy^2 =
-[ 3x^2y + 3xy^2] =
- [-51] =
51
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A over 2+b when a=-2 and b=5
Answer:
-2/7
Step-by-step explanation:
a/2+b when a = -2 and b = 5
~Substitute
-2/2+5
~Simplify denominator
-2/7
Best of Luck!
7.6 more than 1:
8. Carly's dog weighs 25 pounds, and her cat weighs 12 pounds. How much more does
Carly's dog weigh than her cat? What is this problem asking you?
9. There are 56 children who need to be divided into teams of 8. How many children will
be on each team? What is this problem asking you?
10. Crystal went bowling with her family. Her scores were 125, 165, and 106. What was
her total score? What is this problem asking you?
11. Megan added twice as much baking powder to the pancake mix as she was supposed
to. She was supposed to add 5 tablespoons of baking powder. How much baking powder
did she add? What is this problem asking you?
Answer:
Answers below
Step-by-step explanation:
8. is 13 and is asking you how many more pounds does the dog weigh than the cat. it is 13 because if the cat is 12 pounds but the dog is 25 pounds it is just the simple equation of 25 - 12 witch is 13.
9. this problem is asking you what 56 divided by 8 is witch is 7
10. They were asking what 125 + 165 + 106 is witch is 396.
11. There asking what 5 times 2 is. Megan added twice as much baking powder as she was supposed to. if she was supposed to add 5 tablespoons and she put in twice the amount the equation would be 5 times 2 witch equals 10, Therefore your answer is 10.
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Please help!!! Eitan randomly selected volcanoes to travel to and study. After traveling, he had seen 13 cinder cone volcanoes,
18 shield volcanoes, and 6 stratovolcanoes.
Answer:
cinder cone: estimated probability = 0.35
shield: estimated probability = 0.49
stratovolcano: estimated probability = 0.16
Step-by-step explanation:
Given that he had seen 13 cinder cone volcanoes, 18 shield volcanoes, and 6 stratovolcanoes.
So the total number of volcanoes are 13 + 18 + 6 = 37
So the estimated probability of Cinder cone is \frac{13}{37}\approx 0.35
37
13
≈0.35
The estimated probability of Shield is \frac{18}{37}\approx 0.49
37
18
≈0.49
The estimated probability of Stratovolcano is \frac{6}{37}\approx 0.16
37
6
≈0.16
Below is the completed table
on peter's birthday, his brother harry is seventeen years younger than three times peter's age. if peter is seven years younger than his brother harry, how many candles are on peter's cake?
PLEAZE HELPP 50 POINTS If the function f(x) =-3x3 +7x represents the movement of a whale in meters what is the average rate of change of the whale for x=1 and X=3 seconds label your answer
Answer:
The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:
f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4
f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6
The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.
To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."
The length of a bridge is 210 m. The length of each of Robert's paces is 65 cm.
What is the minimum number of full paces that it would take Robert to walk the full length of the bridge?
Using expression 21000 cm ÷ 65 cm/pace, Robert needs to take a minimum of 324 full paces to walk the full length of the bridge.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are grouped together, but not necessarily equated to anything. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple variables and operations.
Now,
To find the minimum number of full paces that Robert needs to take to walk the full length of the bridge, we need to divide the total length of the bridge by the length of each pace.
First, we need to convert the length of the bridge from meters to centimeters because the length of each pace is given in centimeters:
210 m = 21000 cm
Now, we divide the length of the bridge in centimeters by the length of each pace in centimeters:
21000 cm ÷ 65 cm/pace ≈ 323.08 paces
Since Robert cannot take a fraction of a pace, we need to round up to the nearest whole number to get the minimum number of full paces that he needs to take:
323.08 ≈ 324 full paces.
Therefore, Robert needs to take a minimum of 324 full paces to walk the full length of the bridge.
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He loudness of a pile driver is 112 dB. About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.
Complete question :
The loudness of a jack hammer is 96 dB. Its sound intensity is about 0.004.
The loudness of a compactor is 94 dB. Its sound intensity is about 0.0025.
The sound intensity of the jack hammer is about 1.6 times the sound intensity of the compactor.
The loudness of a pile driver is 112 dB. About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.
Answer:
40
Step-by-step explanation:
Given that:
Sound intensity of jackhammer = 0.004
Sound intensity of compactor = 0.0025
Sound intensity of jackhammer is about 1.6 times the sound intensity of a compactor
Each factor of 10 in intensity corresponds to 10dB
Pile driver with loudness of 112dB ; 112 / 10 = 11.2
Hence, 10^11.2 = 1.58489 * 10^11
Hence, sound intensity (I) in watts per m²
I = 1.58489 * 10^11 * 10^-12
I = 1.58489 * 10-1
I = 0.158489
Comparing the intensity of pile driver and jackhammer :
Intensity of piledriver / Intensity of jackhammer
0.158489 / 0.004
= 39.622
= 40 (nearest ten)
Answer:
40
Step-by-step explanation:
Edge 2020
How many meters can the car travel on 3 liters of gas?
Answer:
36,000 meters
Step-by-step explanation:
should a test of statistical significance be conducted before or after computing d and interpreting its value?
Yes, a test of statistical significance be conducted before or after computing d and interpreting its value.
The p-value is an important phrase for hypothesis testing in the context of statistical significance of data.
The p-value is defined as a function of observed sample outcomes that is used to evaluate statistical hypotheses. Before running the test, a threshold value must be chosen.
The significance is a figure that represents the probability that the outcome of a study occurred entirely by chance. The statistical significance can be low or high. It does not always imply practical significance. When a researcher does not use language carefully in their experiment report, the significance may be misconstrued.
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(4 points) Find the auxiliary equation for the following DE: y"" - 4y" + 3y' - 12y = 0.
a. To solve the given initial value problem (IVP) using Laplace transforms, we can apply the Laplace transform to the differential equation and solve for the Laplace transform of the solution.
Taking the Laplace transform of the equation y'(t) + y(t) = (1-3), we have:
sY(s) - y(0) + Y(s) = (1-3)/s
Substituting the initial condition y(0) = 2, we have:
sY(s) - 2 + Y(s) = (1-3)/s
Now, rearranging the equation to solve for Y(s), we get:
Y(s) = (1-3)/s + 2/(s+1)
Simplifying further, we have:
Y(s) = (-2)/s + 2/(s+1)
b. To obtain the solution y(t), we can apply the inverse Laplace transform to Y(s) obtained in part (a).
Taking the inverse Laplace transform, we have:
y(t) = -2 + 2e^(-t)
Therefore, the solution to the given initial value problem is y(t) = -2 + 2e^(-t).
Explanation:
In the first part, we applied the Laplace transform to the differential equation and obtained the equation in terms of the Laplace transform Y(s). By rearranging the equation, we solved for Y(s) in terms of the given Laplace transform expression.
In the second part, we applied the inverse Laplace transform to Y(s) to obtain the solution y(t). The inverse Laplace transform of -2/s gives us a constant term of -2, while the inverse Laplace transform of 2/(s+1) gives us the exponential term 2e^(-t).
Therefore, the solution y(t) = -2 + 2e^(-t) satisfies the differential equation y'(t) + y(t) = (1-3) and the initial condition y(0) = 2.
a. To find the auxiliary equation for the given differential equation y'' - 4y' + 3y' - 12y = 0, we can substitute y = e^(rt) into the equation, where r is an unknown constant.
Substituting y = e^(rt) into the differential equation, we get:
r²e^(rt) - 4re^(rt) + 3e^(rt) - 12e^(rt) = 0
Factoring out e^(rt), we have:
e^(rt)(r² - 4r + 3 - 12) = 0
Simplifying further, we obtain:
e^(rt)(r² - 4r - 9) = 0
Therefore, the auxiliary equation for the given differential equation is r² - 4r - 9 = 0.
b. The auxiliary equation plays a crucial role in finding the solutions to the given differential equation. By solving the auxiliary equation, we can determine the types of solutions and their behavior.
The auxiliary equation for the given differential equation y'' - 4y' + 3y' - 12y = 0 is r² - 4r - 9 = 0. This is a quadratic equation in terms of the unknown constant r.
To solve the quadratic equation, we can use various methods such as factoring, completing the square, or using the quadratic formula. In this case, the quadratic equation does not factor easily, so we can use the quadratic formula:
r = (-(-4) ± √((-4)² - 4(1)(-9))) / (2(1))
Simplifying further, we have:
r = (4 ± √(16 + 36)) / 2
r = (4 ± √52) / 2
r = (4 ± 2√13) / 2
r = 2 ± √13
Therefore, the solutions to the auxiliary equation are r₁ = 2 + √13 and r₂ = 2 - √13.
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What formula is used to find the side lengths?
ANSWER:
The Pythagorean theorem is used to find the hypotenuse of a triangle.
=> AC² = AB² + BC²
In squares, the length of the side can be calculated by finding the square root of the area.
In a species of wildflower, some plants produce pink flowers while other plants produce white flowers. In a cross between two pink wildflowers, 77% of the offspring produced pink flowers and 23% produced white flowers. If two wildflower plants with white flowers were crossed, what percentage of their offspring would most likely produce pink flowers?
The expected percentage of their offspring that would produce pink flowers would be 0%. This is because both the parents that are involved in the cross produce only white flowers and therefore the offspring produced as a result of the cross are expected to only produce white flowers.
However, if the offspring from the cross between the two white flower producing wildflowers were to be crossed with another wildflower population that has pink flowers, there is a chance that some of the offspring from that cross would produce pink flowers. In the given scenario, the cross is being made between two white flower producing wildflowers. Since both the parents involved in the cross produce only white flowers, there is no chance of their offspring producing pink flowers.
The color of the flowers in the offspring is determined by the genetic makeup of the parents that are involved in the cross.In the case of the given wildflowers, the fact that 77% of the offspring produced by a cross between two pink wildflowers produced pink flowers while 23% produced white flowers indicates that the gene for pink flowers is dominant over the gene for white flowers. This is because the gene for pink flowers was passed down to more than three-quarters of the offspring in the cross between the two pink wildflowers. The gene for white flowers, on the other hand, was passed down to only a quarter of the offspring.Hence, if the offspring from the cross between the two white flower producing wildflowers were to be crossed with another wildflower population that has pink flowers, there is a chance that some of the offspring from that cross would produce pink flowers.
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Select whether the model is an angle of elevation or an angle of dep270 ITCMathBits.comB
Explanation:
The term angle of depression is defined as the angle from the horizontal line downward to an object. An observer's line of sight would be below the horizontal.
For angle of elevation, an observer's line of sight would be above the horizontal.
According to the diagram shown; The diagram with angle 27degrees models angle of depression while that of angle 25 degrees models an angle of elevation.
Mrs. Apple just bought a new dining room table. She needs to make a tablecloth for decoration. What amount of fabric should she buy if the table has a diameter of 5 feet? Choose the equation that would best help solve this problem.
Answer:
A = π x 2.5 x 2.5
Step-by-step explanation:
Suzanne walks four miles every third day. What is the fewest number of miles she can walk in February
36 miles is the fewest number of miles she can walk in February
There are 28 days in February.
Every third day is 28/3 = 9.333 = 9 days of walking.
since she walks four miles,
9*4 = 36
Hence, 36 miles is the fewest number of miles she can walk in February
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Umm little help here, please! image is attached please show the work
Answer: See below
Step-by-step explanation:
a) 3x-6y=-12
x-2y=-8 --> x=-8+2y
3x-6y=-12
3(-8+2y)-6y=12
-12+6y-6y=-12
-24=-12
The statement is false for any value of y
b) If you solve the equations for y into slope-intercept form, they have the same slope
--> 3x-6y=-12
6y=12-3x
6 ÷ (6y=-12+3x) ÷ 6
y=1/2x+2
--> y=1/2x+2
x-2y=-8
-2y=-8-x
2 ÷ (2y=8+x) ÷ 2
y=1/2x+4
Since the slopes of the 2 lines are the same, they are parallel, and will never intersect
This camera was on sale for 20% off.
If Alex paid $220, what was the full original price?
Answer: The full price was 275
You just purchased a share of Northstar Sports for $92.79. You expect to receive a dividend of $5.00 in one year. If you expect the price after the dividend is paid to be $94.78, what total return do you expect to earn over the year? What do you expect to be your dividend yield? What do you expect to be your capital gain rate? a. If you expect the price after the dividend is paid to be $94.78, what total return do you expect to earn over the year? Your expected total return to earn over the year is 7.53 %. (Round to two decimal places.) b. What do you expect to be your dividend yield? Your expected dividend yield is%. (Round to two decimal places.)
To predict a linear regression score, you first need to train a linear regression model using a set of training data.
Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,
A higher regression score indicates a better fit, while a lower score indicates a poorer fit.
To predict a linear regression score, follow these steps:
1. Gather your data: Collect the data p
points (x, y) for the variable you want to predict (y) based on the input variable (x).
2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).
3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)] Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.
4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.
5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.
6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging in the x value into the equation. The resulting y value is your predicted linear regression score.
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PLS HELP I WAS SUPPOSE TO SO THIS TODAY BUT I FELL ASLEEP AND IN HAVING TROUBLE
A box has 15 candies in it: 9 are butterscotch, 2 are taffy, and 4 are caramel. (Each candy falls into only one of these categories.) Charmaine wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is butterscotch and the second candy is taffy? Do not round your intermediate computations. Round your final answer to three decimal places. (If necessary, consult a list of formulas.)
The probability that the first candy selected is butterscotch and the second candy is taffy can be calculated as the product of the probabilities of these two events occurring.
First, let's calculate the probability of selecting a butterscotch candy as the first candy. There are 9 butterscotch candies out of a total of 15 candies, so the probability is 9/15.Next, for the second candy to be taffy, we need to consider that one butterscotch candy has already been selected and removed from the box. Therefore, there are 14 candies remaining in the box, including 2 taffy candies. Hence, the probability of selecting a taffy candy as the second candy is 2/14.
To find the probability of both events occurring, we multiply the probabilities together: (9/15) * (2/14) = 18/210.Simplifying this fraction, we get 3/35.Therefore, the probability that the first candy selected is butterscotch and the second candy is taffy is 3/35, which is approximately 0.086 or rounded to three decimal places.
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Under a dilation centered at the origin, the vertex, (−2, 4), of a polygon is moved to the point (4, −8) . What is the scale factor of the dilation?
Answer:
-2
Step-by-step explanation:
I took the quiz.
The scale factor of the dilation is -2.
How does dilation works?Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.
It's also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.
It's like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).
Given that Under a dilation centered at the origin, the vertex, (−2, 4), of a polygon is moved to the point (4, −8) .
Then the scale factor of the dilation
(-2k , 4k )= (4, −8)
Thus, -2k = 4
k = -2
Hence, the scale factor of the dilation is -2.
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Why is weighing using a Tared Container not appropriate for for quantitative preparation. How could this impact the results.
Weighing using a tared container is not appropriate due to the potential for errors and inaccuracies. This method can impact the results by introducing uncertainties in the measurements.
Using a tared container involves placing the substance to be weighed on a container that has already been weighed and then subtracting the weight of the container to obtain the weight of the substance alone. While this method is commonly used for qualitative analysis or when the accuracy requirements are not strict, it is not suitable for quantitative preparation where precise measurements are essential.
The use of a tared container introduces several potential sources of error. First, the accuracy of the tare weight might not be exact, leading to uncertainties in subsequent measurements. Additionally, the tare weight may change over time due to factors like evaporation or contamination, further affecting the accuracy of subsequent measurements. Moreover, the process of transferring the substance to the tared container introduces the risk of loss or gain of material, leading to errors in the final measurements.
Overall, relying on weighing with a tared container for quantitative preparation can result in inaccurate quantities of the substance being weighed, compromising the reliability and reproducibility of experimental results. Therefore, more precise weighing techniques, such as using calibrated weighing balances or analytical techniques, should be employed for quantitative preparations.
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Perform the operation
(10x² – x + 1) – (9x – 2)
Help ASAP please
Answer:
10x^2-10x+3
Step-by-step explanation:
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What is the inverse of the function below?
f(x) = x/4-2
The inverse of the linear function can be written as:
f⁻¹(x) = 4*(x + 2)
So the correct option is A.
How to find the inverse of the linear function?Here we want to find the inverse of the linear function:
f(x) = x/4 - 2
Remember that two functions are inverses if the composition is equal to the identity, this means that if f⁻¹(x) is the inverse, we must have that:
f(f⁻¹(x)) = x
Replacing the actual function we will get:
f⁻¹(x)/4 - 2 = x
Solving for the inverse we will get:
f⁻¹(x)/4 = x + 2
f⁻¹(x) = 4*(x + 2)
So the correct option is the first one.
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I am an odd number. Take away one letter and I become even. What number am I?
Answer:
I think u old number is 7 it is my luck number
The idea that group work theories are appropriate for all clients all the time is a(n)? empirical truth professional tenet myth lie
The idea that group work theories are appropriate for all clients all the time is a myth (Third option).
About Group Process:
The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.
Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.
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Point M is the midpoint of line segment CD,
shown below.
What are the coordinates of point M?
C (6,10)
M
D (20, 18)
Answer:
M(13, 14)-------------------------
Each coordinate of the midpoint is the average of endpoints:
x = (6 + 20)/2 = 26/2 = 13y = (10 + 18)/2 = 28/2 = 14Therefore M is (13, 14).
A length of wire was cut into 8 equal segments. If the wire was 48 inches long, how long was one segment?
Answer: 6
Explanation: 6x8