Answer:
Step-by-step explanation:
By triangle sum theorem,
Sum of all angles of a triangle is 180°.
m∠1 + m∠2 + m∠3 = 180°
(m∠1 + m∠3) + m∠2 = 180°
2(m∠1) + 70° = 180° {Given → m∠1 = m∠3]
2(m∠1) = 110°
m∠1 = 55°
Therefore, m∠1 = m∠3 = 55°
An ocean liner leaves port at 9:00 a.m. traveling directly out to sea at 22 miles per hour. A ferry leaves port at 9:30
a.m. traveling the same direction at 28 miles per hour. Use this information to complete the sentences.
A pair of parametric equations representing the paths of the boats are
From the time the ocean liner leaves until the ferry overtakes it is minutes at a distance from the port of
approximately miles.
Answer:
x=22t and y=28(t-0.5)
140
51
Step-by-step explanation:
right on edg
Answer:
A pair of parametric equations representing the paths of the boats are
✔ x = 22t and y = 28(t – 0.5) (Negative 0.5).
From the time the ocean liner leaves until the ferry overtakes it is
✔ 140.
minutes at a distance from the port of approximately
✔ 51 miles.
Step-by-step explanation:
Edge 2022
raindrops are falling at an average rate of 20 drops per square inch per minute. what would be a reasonable distribution to use for the number of raindrops hitting a particular region measuring 5 square inches in a minute? why? using your chosen distribution, compute the probability that the region has no rain drops in a given 6-second time interval.
The number of raindrops hitting a particular region can be modeled using the Poisson distribution. The Poisson distribution is commonly used to describe the number of events occurring in a fixed interval of time or space when these events happen randomly and independently with a known average rate. In this case, the average rate is given as 20 drops per square inch per minute. The probability that the region has no raindrops in a given 6-second time interval is approximately 0.7165
To compute the probability that the region has no raindrops in a given 6-second time interval, we need to convert the rate to match the time interval. Since the rate is given per minute, we can divide it by 60 to get the rate per second: λ = 20/60 = 1/3 drops per square inch per second.
Using the Poisson distribution, the probability of observing exactly k events in a given time interval is given by the formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where e is Euler's number (approximately 2.71828), λ is the average rate, and k is the number of events.
In our case, we want to find the probability that the region has no raindrops in a 6-second time interval, which corresponds to k = 0.
P(X = 0) = (e^(-1/3) * (1/3)^0) / 0! = e^(-1/3)
Using a calculator, we can evaluate e^(-1/3) ≈ 0.7165.
Therefore, the probability that the region has no raindrops in a given 6-second time interval is approximately 0.7165 or 71.65%.
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-2x - 5x + 3 - 8 please help
Answer:
-7x - 5
Step-by-step explanation:
Combine like terms.
May someone please help me with this :)
Answer:
3,080 cm
Step-by-step explanation:
simple -. -
Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. f(x) = 4x (3) = f(5) = f(-2) = f(0.4) =
Using the function f(x) = 4x, we find that f(3) = 12, f(5) = 20, f(-2) = -8, and f(0.4) = 1.6.
To evaluate the function f(x) = 4x at the indicated values, we can use a calculator to perform the calculations.
f(3):
Multiply 3 by 4: 3 * 4 = 12
The value of f(3) is 12.
f(5):
Multiply 5 by 4: 5 * 4 = 20
The value of f(5) is 20.
f(-2):
Multiply -2 by 4: -2 * 4 = -8
The value of f(-2) is -8.
f(0.4):
Multiply 0.4 by 4: 0.4 * 4 = 1.6
The value of f(0.4) is 1.6.
The function simply multiplies the input value by 4 to determine the output value.
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The question is in the picture.
Answer:
arc CD = 160°
Step-by-step explanation:
The measures of the arcs on the circle = 360° , then
arc CD = 360 - AC - AD = 360 - 3x - 7x = 360 - 10x
--------------------------------------------------------------------------
The measure of the secant- tangent angle ABC is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] (7x - 3x) = 40 ( multiply both sides by 2 to clear the fraction )
7x - 3x = 80
4x = 80 ( divide both sides by 4 )
x = 20
Then
CD = 360 - 10x = 360 - 10(20) = 360 - 200 = 160°
How many residuals lie outside the 95% prediction bands? According to the SRM, how many of these should lie above and how many should lie below the estimated regression line?
The number of residuals outside the 95% prediction bands depends on the specific data and regression model. The explanation below provides general insights.
The number of residuals lying outside the 95% prediction bands can vary depending on the data and the estimated regression model. In a simple linear regression, the prediction bands represent the range within which future observations are expected to fall with 95% confidence.
Ideally, if the model assumptions are met and the regression is a good fit, we would expect only about 5% of the residuals to fall outside the prediction bands by chance. However, if the assumptions are violated or the model is not appropriate, more residuals may deviate beyond the bands.
The distribution of residuals above or below the estimated regression line depends on the symmetry of the errors. If the errors are normally distributed and the model is unbiased, roughly half of the residuals lying outside the prediction bands should be above the line, and the other half should be below the line.
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please help.
I need which letters to click
Ethan makes punch by mixing orange juice with
sparkling water. He uses the same ratio of orange juice
to sparkling water each time he makes punch. The table
shows some of the amounts of orange juice and
sparkling water he uses for different amounts of punch.
Orange Juice (fl oz) 7 21 28 ?
Sparkling Water (fl oz) 4 12 16 28
If Ethan uses 28 fl oz of sparkling water, how much orange juice will he use and what will be the total amount of punch?
Use the number pad to enter your answers in the boxes.
Ethan will use ____
fl oz of orange juice, and he will have a total of ___
fl oz of punch.
Answer:
Ethan will use 49
fl oz of orange juice, and he will have a total of 77
fl oz of punch.
Step-by-step explanation:
He uses a ratio of 7 to 4 of orange juice to sparkling water.
7/4 = ?/28
4 * ? = 7 * 28
Divide both sides by 4.
? = 7 * 7
? = 49
He will use 49 fl oz of orange juice.
The total amount made is: 49 fl oz + 28 fl oz = 77 fl oz
Answer:
Ethan will use 49
fl oz of orange juice, and he will have a total of 77
fl oz of punch.
Lollipops cost 12p each, but I get 3 for 30p. What is the maximum number of lollipops I can buy if I have £2 to spend?
Answer:
18 lolly pops
Step-by-step explanation:
3 = 30p
3x6 = 1.80
= 18
Translate the phrase into an inequality:
Seven plus a number x is at most twenty
At most means less than or equal to:
7 + x ≤ 20
give a database of the results of an election, find the number of seats won by each party
To find the number of seats won by each party from a database of election results, we need the specific information about the parties, the candidates, and the corresponding vote counts or seat allocations.
With that information, we can perform calculations or queries to determine the number of seats won by each party.
Here's a general outline of the steps involved:
Obtain the election database or data that includes information on parties, candidates, and their respective vote counts or seat allocations.
Analyze the database structure to identify the relevant tables or fields
that store the necessary information.
Use database query or analysis tools to extract the relevant data. Write a query or use filtering mechanisms to retrieve the party names, candidate information, and corresponding vote counts or seat allocations.
Perform calculations or aggregations based on the data retrieved to determine the total number of seats won by each party. This can involve summing the vote counts or seat allocations for each party.
Present or display the results, showing the number of seats won by each party in the election.
Please provide the specific database structure or information about the parties, candidates, and vote counts if you have them, and I can assist you further in generating the desired results.
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The length of a rectangular frame is 15 inches and the width of the frame is 8 inches. What
is the length of the diagonal of this frame in inches?
Record your answer. Be sure to use the correct place value.
Estimate the area of tje fan if m
Answer:
Area of the given fan is 763.4 cm²
Step-by-step explanation:
Area of a sector in a circle = [tex]\frac{\theta}{360}(\pi r^2)[/tex]
Here, angle θ = Central angle subtended by the arc
r = Radius of the circle
Since, fan is in the form of a sector of a circle with radius = 27 cm
Measure of the central angle subtended by the arc FN = ∠FAN = 120°
Area of the fan = [tex]\frac{120}{360}(\pi )(27)^2[/tex]
= [tex]\frac{729\pi }{3}[/tex]
= 243π
= 763.407
≈ 763.4 cm²
Therefore, area of the given fan is 763.4 cm²
Para resolver un sistema de ecuaciones lineales 2x2 por el método de sustitución se debe tener en cuenta:
A) consiste en despejar la misma incógnita en las dos ecuaciones y después igualar los resultados. En primer lugar, elegimos la incógnita que deseamos despejar. En este caso, empezaré por la «x» y despejo la misma en ambas ecuaciones.
B) debemos saber representar las gráficas de las rectas. Nosotros lo haremos uniendo puntos calculados previamente. Terminaremos con un sistema de dos inecuaciones (o desigualdades). En este caso, la solución del sistema es la intersección de dos regiones del plano.
C) es un método lineal ya que no se basa en despejes, se utilizan procesos algebraicos estructurados.
D) consiste en despejar o aislar una de las incógnitas (por ejemplo, x ) y sustituir su expresión en la otra ecuación. De este modo, obtendremos una ecuación de primer grado con la otra incógnita, y . Una vez resuelta, calculamos el valor de x sustituyendo el valor de y que ya conocemos.
AYUDA PLS
Answer:
El método de igualación consiste en despejar la misma incógnita en las dos ecuaciones y después igualar los resultados.
Los pasos a seguir son los siguientes:
sistema de ecuaciones
En primer lugar, elegimos la incógnita que deseamos despejar. En este caso, empezaré por la «x» y despejo la misma en ambas ecuaciones.
x+y=7; x=7-y
5x-2y=-7; 5x=2y-7
x=(2y-7)/5
Una vez hemos despejado, igualamos:
7-y = (2y-7)/5
5.( 7-y) = (2y -7)
35 -5y= +2y -7
42=7y
y=42/7=6
y=6
Por último, sustituimos el valor que hemos calculado despejando la otra incógnita en una de las ecuaciones iniciales.
SOMEONE HELPPP
What is the classification of the figure?
What is the factored form of 6x²+13x+5?
Answer:
x1=-1/3 and x2=-1/5
3(3x+1)+2(5x+1)
3x+1=0,5x+1=0
×=-1/4 x=-1/5
If shooting in different light sources each light source should have a different custom color profile. True False
The statement "If shooting in different light sources each light source should have a different custom color profile" is False.
Shooting in different light sources does not necessarily require different custom color profiles. The purpose of a color profile is to ensure accurate color reproduction across different devices and environments. While different light sources may have different color temperatures and characteristics, modern cameras and editing software often provide options to adjust white balance and color settings to account for different lighting conditions.
These adjustments can help achieve consistent and accurate colors without the need for separate custom color profiles for each light source. However, in certain professional or specialized applications, such as high-end photography or color-critical work, custom color profiles may be created to fine-tune color accuracy based on specific lighting conditions.
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a sine function has an amplitude of 3, a period of π, and a phase shift of pi over 2 period what is the y-intercept of the function?
The y-intercept of the sine function with an amplitude of 3, a period of π, and a phase shift of π/2 is 0.
The general form of a sine function is y = A×sin(Bx - C) + D, where A represents the amplitude, B determines the period, C is the phase shift, and D is the vertical shift.
In this case, the given amplitude is 3, indicating that the maximum value of the function is 3 and the minimum value is -3.
The period is π, which means the function completes one full cycle in π units of x.
The phase shift is π/2 period, which shifts the graph to the right by π/2 units.
Since the y-intercept is the point where the graph intersects the y-axis (x = 0), and the sine function passes through the origin (0, 0), the y-intercept is 0.
Therefore, the y-intercept of the given sine function is 0.
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Choose the function whose graph is given by:
O A. y=tan(x + 2) - pi
O B. y=tan(x - pi) + 2
O C. y=tan(x-pi) - 2
D. y=tan(2(x + pi)) + 2
it’s b!!!
Answer:
d
Step-by-step explanation:
y=tan (2(x+2)-2, I think that is it
Answer:
y=tan(x-pi)-2
Step-by-step explanation:
How would you use the unit rate to find the number of cups of dry rice you would need to serve 50 people?
the unit rate is 3 people/1 cup of rice.
Answer:
3 people/1 cup
50/3 = 16.68 cups of dry rice
Solve the differential equation (D2 + 4)y=6 sin2x +3x2 =
The general solution to the differential equation (D^2 + 4)y = 6sin(2x) + 3x^2 is y = A sin(2x) + B cos(2x) + (3/4)x^2.
To solve the given differential equation (D^2 + 4)y = 6sin(2x) + 3x^2, where D represents the derivative operator, we can use the method of undetermined coefficients.
The homogeneous solution to the equation is y_h = A sin(2x) + B cos(2x), where A and B are arbitrary constants.
To find the particular solution, we assume y_p = Cx^2 + Dx + E as it contains the same form as the non-homogeneous term. By substituting y_p into the equation and comparing coefficients, we find that C = 3/4.Therefore, the general solution to the differential equation is y = A sin(2x) + B cos(2x) + (3/4)x^2, where A and B are arbitrary constants. This solution accounts for both homogeneous and particular solutions.
The specific values of A and B can be determined by applying initial or boundary conditions if given.
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Given that sin(u) = 5/13 for 0 <= u <= π and tan(v)= -3/4 for π/2 <= v <= π. Find the values of Sin (u+v).
The value of sin(u+v) is -16/13. The value of sin(u+v) can be determined using trigonometric identities and the given information. We are given that sin(u) = 5/13 for 0 ≤ u ≤ π and tan(v) = -3/4 for π/2 ≤ v ≤ π.
To find sin(u+v), we need to use the sum of angles formula for sine. According to this formula, sin(u+v) = sin(u)cos(v) + cos(u)sin(v).
From the given information, we know the value of sin(u) = 5/13. To find cos(u), we can use the Pythagorean identity [tex]sin^2(u) + cos^2(u) = 1[/tex]. Plugging in the value of sin(u), we have [tex](5/13)^2 + cos^2(u) = 1[/tex]. Solving for cos(u), we find cos(u) = 12/13.
Similarly, we know that tan(v) = -3/4. Using the identity tan(v) = sin(v)/cos(v), we can solve for sin(v) and cos(v). We have sin(v)/cos(v) = -3/4, which implies sin(v) = -3 and cos(v) = 4.
Now we have all the values needed to calculate sin(u+v). Substituting the known values into the sum of angles formula, we get sin(u+v) = (5/13)(4) + (12/13)(-3) = 20/13 - 36/13 = -16/13.
Therefore, the value of sin(u+v) is -16/13.
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Suppose we are given a series [=1(-1)+1 9n(x), where for each fixed x € R, we have 91() > 92(x) > 93(x) > ..0. Assume furthermore that 91(2) is bounded on R, and that the In(x) converge pointwise to 0. Prove that the series converges uniformly on R.
|In(x)| < ε/M for all x ∈ R, we can bound the above expression by:|91(n+1)(x) + 91(n+2)(x) + ...| ≤ 91(n+1)ε/M + 91(n+2)ε/M + ... = ε.This shows that the series converges uniformly on R.
We must demonstrate that for any given > 0, there exists a positive integer N such that the difference between the partial sum Sn(x) and the limit L(x) for all x R is less than to demonstrate that the series converges uniformly on R.
Since 91(2) is limited on R, let M be an upper headed for 91(2). Since the In(x) unite pointwise to 0, for any ε > 0, there exists a positive number N with the end goal that for all n > N, |In(x)| < ε/M for all x ∈ R.
Presently, for n > N and for all x ∈ R, we have:
|Sn(x) - L(x)| = |(∑ i=1 to n 91(i)(x)) - 0| = |91(n+1)(x) + 91(n+2)(x) + ...|
Since |In(x)| < ε/M for all x ∈ R, we can bound the above articulation by:
|91(n+1)(x) + 91(n+2)(x) + ...| ≤ 91(n+1)ε/M + 91(n+2)ε/M + ... = ε
This shows that the series combines consistently on R.
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-1.2k + 3.9 - g + .5g + 7 + .3k
Answer:
hi
Step-by-step explanation:
You are given two pairs of triangles. For the first pair of triangles, each side and angle of one triangle is congruent to the corresponding side and angle of the other. You show that rigid motions can transform one triangle so that it matches up with the other. For the second pair of triangles, you show that rigid motions can transform one triangle so that each angle or side of one triangle matches exactly with a corresponding angle or side of the other triangle. What have you proved?
Options:
a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.
b) If two triangles can be matched up exactly using rigid motions, then the corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Step-by-step explanation:
For both pairs of triangles, what you proved is how to use rigid motions (i.e. rigid transformations) to make congruent shapes.
When rigid transformation is applied to a shape, the image (i.e. result) of the transformation produces an exact shape (i.e. equal corresponding angles and corresponding sides), meaning that the side lengths and the angles of the preimage (before transformation) and the image (after transformation) is unaltered.
Option (c) is true
Simplify: 121/11 + 3(4)/2
Please and thank you. :)
Answer:
17
Step-by-step explanation:
I don't know the explanation, but hoped this helped.
For many relatively simple probability questions such as these, you should find that the math and calculations involved are not at all onerous. The trick is recognizing which concepts apply, and therefore which tools (e.g. formulas) are most appropriate for the job. It is equally important to recognize when the tools in your toolbox do NOT apply! This is so that when looking at data in the real world, or if you are looking at someone else's interpretation of data, you recognize when people are not using or interpreting the data appropriately.
For any confidence interval questions, you should provide a properly formatted confidence interval statement as your answer.
In solving simple probability questions, the calculations involved are usually straightforward. The key lies in identifying the applicable concepts and selecting the appropriate tools or formulas. Equally important is recognizing when these tools do not apply, enabling proper interpretation of data.
Understand the problem: Carefully read and comprehend the question to determine what information is given and what needs to be calculated. Identify the relevant concepts and tools that can be utilized.
Select the appropriate formula: Based on the problem statement and the involved concepts, choose the relevant formula or method to calculate the probability or confidence interval. Examples include the addition rule, multiplication rule, or Bayes' theorem.
Apply the given information: Substitute the known values into the formula, ensuring proper assignment and consistency of units.
Perform the calculations: Use mathematical operations to compute the desired probability or confidence interval. Take note of any special conditions or considerations mentioned in the problem.
Provide a clear answer: Express the result in a well-formatted manner. For probability questions, the answer may be a single value or a range, depending on the problem. Confidence interval questions require a properly formatted statement that includes the estimated parameter, range, and confidence level.
Validate and interpret the answer: Review the calculations for accuracy, and round the answer if necessary. Additionally, interpret the result within the context of the problem, providing explanations or conclusions as needed.
By practising with a variety of probability problems and confidence interval questions, you can improve your ability to identify relevant concepts and select the appropriate tools to solve them accurately. Furthermore, this practice will enhance your skills in recognizing when others may be misusing or misinterpreting data in real-world scenarios.
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Which of the following are necessary conditions for the hypothesis test for the slope of the least squares regression line? (Select all that apply.) There is equal variance around the regression line for all x. The distribution of x is normal. The observations are independent. The sampling distribution of x is approximately normal. Data are from a random sample or experiment. The responses, y, for any value of x vary according to a normal distribution. The true relationship between the variables is linear. The parameter of interest is the true slope, ß
The conditions for hypothesis test for slope of least squares regression line are observations are independent, data is from random sample, the true relationship between variables is linear. So, correct options are c, e, f, g, h.
c) The observations are independent: This condition is necessary to ensure that the observations are not influenced by each other and that the regression estimates are not biased.
e) Data are from a random sample or experiment: Random sampling helps to ensure that the sample is representative of the population and allows for generalization of the results. In an experiment, random assignment helps establish causal relationships.
f) The responses, y, for any value of x vary according to a normal distribution: This assumption is needed to perform hypothesis tests and construct confidence intervals for the slope. It is usually assumed that the errors or residuals in the regression model are normally distributed.
g) The true relationship between the variables is linear: This assumption assumes that the relationship between the independent variable (x) and the dependent variable (y) can be adequately represented by a straight line.
h) The parameter of interest is the true slope, β: The hypothesis test focuses on testing whether the estimated slope coefficient significantly differs from zero, which represents the null hypothesis.
The remaining options (a, b, d) are not necessary conditions for the hypothesis test for the slope of the least squares regression line. They may be assumptions or conditions related to the regression model but are not directly tied to the hypothesis test for the slope.
So, correct options are c, e, f, g, h.
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To solve for x in the equation x + 3 = 5, you would...
answer/ step-by-step explanation:
hi there!
the question is asking us to solve for x for the equation
x + 3 = 5
first we need to get all the numbers on to one side of the equal sign while the other side has all the variable
in order to do that we need to subtract 3 on both sides
x + 3 = 5
- 3 - 3
and that leaves us with our answer!
x = 2
i hope this helps you :) if you need anymore help or if i did something wrong then please tell me! have a good day :)