Find the measure of this angle, and explain your answer.

The expression cos (125°) - cos 55° cos 35° cos 55° can be written as cos (55°) + cos (55°) cos (35°) cos (55°).

cos (125°) can be rewritten as cos (180° - 125°). Similarly, cos (35°) can be rewritten as cos (180° - 35°). Therefore, the expression can be written as:

cos (180° - 125°) - cos (55°) cos (180° - 35°) cos (55°)

Simplifying further, we have:

cos (55°) - cos (55°) cos (145°) cos (55°)

Since 145° is the supplement of 35°, we can rewrite it as:

cos (55°) - cos (55°) cos (180° - 35°) cos (55°)

Now, cos (180° - 35°) is equal to -cos (35°). Therefore, the expression becomes:

cos (55°) + cos (55°) cos (35°) cos (55°)

Hence, the expression as a function of an acute angle is:

cos (55°) + cos (55°) cos (35°) cos (55°)

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The probability of the team having at most 1 injury in the game can be calculated using a Poisson distribution.

To find the probability of the team having at most 1 injury in a typical football game, we can use a Poisson distribution. The Poisson distribution is commonly used to model the occurrence of rare events, such as injuries in this case.

The parameter for the Poisson distribution is the average number of injuries per game, which is given as 3.2.

Let's denote the random variable X as the number of injuries in a game. We need to calculate the probability P(X ≤ 1), which represents the probability of having at most 1 injury.

Using the Poisson distribution formula, we can compute this probability:

P(X ≤ 1) = P(X = 0) + P(X = 1)

Using the Poisson probability mass function, we substitute the values into the formula and calculate the probability.

The result will be the probability that the team will have at most 1 injury in the game.

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The triangle is an isosceles right-angle triangle. Then the hypotenuse of the triangle will be 3 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of one angle of right-angle is 45°. Then the right triangle is an isosceles right-angle triangle.

Then the hypotenuse is given by the sine of angle 45°. Then the equation is given as,

sin 45° = 3√2 / H

1/√2 = 3√2 / H

H = 3√2 x (1 / √2)

H = 3 units

The triangle is an isosceles right-angle triangle. Then the hypotenuse of the triangle will be 3 units.

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Answer:

the answer for the question is D,experiment

The kind of statistical study that Thad Conducted is called; Experiment

We ae told that we want to determine the cleaner that has the best effectiveness.

Now, since he compares the result of washing with let's say brand A to the result of washing with maybe brand B, then we can say that it is called an experiment due to the fact that it involves the procedure used to determine the efficacy or likelihood of something.

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True. The random() method is a function that generates a random floating-point number between 0 (inclusive) and 1 (exclusive).

This means that the generated number will be greater than or equal to 0 and less than 1. For example, a call to random() might return a value like 0.342341, 0.859203, or 0.000001.

Here is an example of how the random() method can be used in Python to generate a random float between 0 and 1:

import random

# Generate a random float between 0 and 1

x = random.random()

print(x)

The output of this code might be something like 0.342341 or 0.859203.

Therefore, it's true that The random() method is a function that generates a random floating-point number between 0 (inclusive) and 1 (exclusive).

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This means that the generated number will be greater than or equal to 0 and less than 1. For example, a call to random() might return a value like 0.342341, 0.859203, or 0.000001.

Here is an example of how the random() method can be used in Python to generate a random float between 0 and 1:

import random

# Generate a random float between 0 and 1

x = random.random()

print(x)

The output of this code might be something like 0.342341 or 0.859203.

Therefore, it's true that The random() method is a function that generates a random floating-point number between 0 (inclusive) and 1 (exclusive).

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A wire is cut into two pieces, one piece bent into square and other piece will be bent into circle. Therefore, the minimum length of wire that can be used is 43 m.

The relationships between the radius of a circle and its circumference and area are :

                                           C = 2πr

                                            A = πr²

The relationships between the side length of a square and its perimeter and area are :

                                        P = 4s

                                        A = s²

So, the length of wire will be

                         W= C + P

                        W = 2πr + 4s

Subject to the constraint that the sum of areas is 144 m²:

                                 πr² + s² = 144

Using the method of Lagrange multipliers to find the extremes of wire length, we want to set the partial derivatives of the Lagrangian (L) to zero.

                       L = 2πr + 4s + λ(πr² +s² -144)

                   ∂L/∂r = 0 = 2π +2πλr      ------------------------------- (1)

                   ∂L/∂s = 0 = 4 +2λs           ------------------------------- (2)

                   ∂L/∂λ = 0 = πr² +s² -144    -------------------------------- (3)

Solving for λ, we find,

                   1 +λr = 0      ---------------------------- (4)

                ⇒  λ = -1/r      ----------------------------- (5)

Substituting into equation (2), we get,

                  4 + 2(-1/r)s = 4

               ⇒  s/r = 2  -------------------------------- (6)

This tells us the maximum wire length is that which makes the circle diameter equal to the side of the square.

Substituting the relation s=2r into the area constraint, we find,

                          πr² +(2r)² =144  

                      ⇒  r = √(144/(π+4))

                      ⇒  r= 12/√(π+4) ≈ 2.068965 . . . m

∴ The minimum wire length will be required when the entire area is enclosed by the circle. In that case,

                           πr² = 144

                        ⇒  r = √(144/π)

           and,           C = 2πr

                         = 2π√(144/π)

                         = 24√π ≈42.5388 . . m

rounding up the minimum value 42.5388... in 43.

∴ The minimum wire length will be required is 43 m

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Answer:

fraction: 3 divided by 10 = 3/10

decimal: 3 divided by 10 = 0.3

word form: three tenths

Step-by-step explanation:

Not really sure how to explain but it's basically number of kickballs divided by total number of balls.

Answer:

Sam made 21 shots, and Wil made 27 shots.

Answer: 1/2

Step-by-step explanation:

1) Put the equation into y=kx form

- add 4x to both sides

- divide by 8 on both sides to get y=1/2x

2) k is the constant of proportionality

Answer: $50

Step-by-step explanation:

The researcher is arranging experimental units in groups that are similar to each other. That is the definition of Blocking in statistics.

So the answer is B. Blocking.

Answer:

y=-1x-6

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=-1(x-(-1)

y+5=-1(x+1)

y+5=-1x-1

y=-1x-5-1

y=-1x-6

Answer: ok so i think the answer is 4.2 or 5.2 if im wrong then well sorry

Step-by-step explanation:

Answer:

I think it is B

Step-by-step explanation:

Answer:

a) 5

b) 30

c) 40

Step-by-step explanation:

(no entiendo mucho espanol pero voy a ayudar...)

a) hay 10 que haces los dos, 30 que solo estudien, y 40 que solo trabajan. Con eso, 80-10-30-40 = 5, y asi tienes 5 personas que no estudian y no trabajan

b) las personas que estudian son 40, y 10 trabajan tambien, asi solo tienes 30 personas que unicamente se dedican a estudiar.

c) las personas que trabajan son 50, y 10 estudian tambien, asi solo tienes 40 personas que unicamente se dedican a estudiar.

The largest interval I over which the solution is defined is (-∞, ∞).               I = (-∞, ∞)

To solve the given initial-value problem, we can use the method of separation of variables as follows:
1. Separate the variables by moving all terms with y to the left side of the equation and all terms with x to the right side:
y/y' = ex/x
2. Integrate both sides of the equation with respect to their respective variables:
∫y/y' dy = ∫ex/x d
ln(y) = ex + C
3. Solve for y:
y = e^(ex + C)
4. Use the initial condition y(1) = 9 to find the value of C:
9 = e^(e + C)
C = ln(9) - e
5. Substitute the value of C back into the equation for y:
y = e^(ex + ln(9) - e)
6. Simplify the equation:
y = 9e^(ex - e)
7. The largest interval I over which the solution is defined is (-∞, ∞), since there are no restrictions on the values of x or y therefore, the solution to the initial-value problem is y(x) = 9e^(ex - e) and the largest interval I over which the solution is defined is (-∞, ∞).

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Answer:

Suppose that P(t) describes the position of Matt over time

Let's define the edge of the pool as our zero in the position axis.

At the beginning, Matt was 3 ft away from the edge, so we have:

P(0s) = 3ft

He walked away for 4 seconds, then he was 12 ft away from the edge.

Then at t = 4s his position was:

P(4s) = 12ft.

So we have two points, (0s, 3ft) and (4s, 12ft).

The graph that describes this situation will be the line that connects those two points.

An example is shown below.

Answer:

0,3 - 4,12

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

(4)^2+3(4)

16 + 12

28

hi <3

i'm not sure where the x fits into this so i'll ignore that part.

simply substitute m into the equation and solve

(4)^2 + 3(4) = 16 + 12 = 28

your answer is 28

hope this helps :)

Answer:

C. -7.4

Step-by-step explanation:

-(5(-2) + 2) + (3(3) + 2(-4.2))

(-10+2) + (9 + -8.4)

-8 + 0.6

-7.4

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer: a) To find the equation of line PS, we first need to find the slope of the line L1 which is given by:

slope = (y2 - y1) / (x2 - x1)

= (3 - 5) / (-2 - 0)

= 2/2

= 1

Since PS is parallel to L1, it also has the same slope. We can now use the point-slope form of the equation of a line to find the equation of PS, using the point P(1,2):

y - y1 = m(x - x1)

y - 2 = 1(x - 1)

y - x + 2 = 0

Therefore, the equation of line PS is y - x + 2 = 0.

b) To find the coordinates of S, we know that S lies on line PS and also on the line passing through points (6,4) and P(1,2). Let's call the coordinates of S as (x,y). Since S lies on line PS, we know that y - x + 2 = 0. We can also use the slope formula to find the slope of line PS:

slope_PS = (y - 2) / (x - 1)

Since PS is parallel to line L1, we know that slope_PS = 1. Therefore, we can write:

(y - 2) / (x - 1) = 1

y - 2 = x - 1

y = x + 1

Now, we can use the fact that S also lies on the line passing through points (6,4) and P(1,2). This line has the equation:

(y - 4) / (x - 6) = (2 - 4) / (1 - 6)

(y - 4) / (x - 6) = -2/-5

(y - 4) / (x - 6) = 2/5

We can solve for y in terms of x:

y - 4 = (2/5)(x - 6)

y = (2/5)x - 8/5 + 4

y = (2/5)x + 6/5

Now, we can set the two equations for y equal to each other, since they both represent the y-coordinate of point S:

x + 1 = (2/5)x + 6/5

Solving for x, we get:

x = 2

Substituting x = 2 into either of the equations for y, we get:

y = 3

Therefore, the coordinates of S are (2,3).

c) To find the coordinates of Q, we can use the fact that PQ is parallel to SR and PS is parallel to QR. This means that PQRS is a parallelogram and its opposite sides are parallel. Since we know the coordinates of P and S, we can find the coordinates of Q and R by adding or subtracting the appropriate vector from P and S.

The vector that we need to add to P to get Q is the same vector that we need to add to S to get R, which is given by the displacement vector PS = <5,1>. Therefore:

Q = P + PS

= <1,2> + <5,1>

= <6,3>

Therefore, the coordinates of Q are (6,3).

d) To find the equation of line L2 which is the perpendicular bisector of line QR, we first need to find the midpoint of QR. The midpoint formula is given by:

midpoint = [(x1 +)]

We can then find the midpoint of QR using the midpoint formula:

midpoint of QR = ((-4 + 1)/2, (7 + 4)/2) = (-1.5, 5.5)

So the slope of L2 is the negative reciprocal of the slope of QR:

slope of L2 = -1/slope of QR = -(7-5)/(1+4) = -2/5

We can use the point-slope form of the equation of a line to find the equation of L2. We know that L2 passes through the midpoint of QR, so we can use the point (-1.5, 5.5):

y - 5.5 = (-2/5)(x + 1.5)

Simplifying and rearranging, we get:

y = (-2/5)x + 7.5

Therefore, the equation of line L2 is y = (-2/5)x + 7.5.

If the expression be 23 x² + 3x + 8 then the constant exists 8.

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.

Let the expression be 23 x² + 3x + 8

then the constant exists 8.

Therefore, the correct answer is option C. 8.

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Answer:

>

Step-by-step explanation:

Cause 750 was the least they could raise

Answer:

>=

Step-by-step explanation:

>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE

The probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.

To calculate the probability of randomly selecting a homeowner and a renter from a small village of 300 residents with 190 homeowners and 110 renters in a sample of 20 residents, follow these steps:
1. Calculate the probability of selecting a homeowner (P(homeowner)).
P(homeowner) = Number of homeowners / Total number of residents = 190 / 300
2. Calculate the probability of selecting a renter (P(renter)).
P(renter) = Number of renters / Total number of residents = 110 / 300
3. Calculate the number of ways to choose 19 homeowners and 1 renter from the sample (Combination).
C(190,19) × C(110,1) = (190! / (19! × (190-19)!)) × (110! / (1! × (110-1)!))
4. Calculate the number of ways to select a random sample of 20 residents (Combination).
C(300,20) = 300! / (20! × (300-20)!)
5. Calculate the probability of selecting 19 homeowners and 1 renter from the random sample of 20 residents.
Probability = (C(190,19) × C(110,1)) / C(300,20)
By calculating these values, you will find the probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.

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The correct answer is (c) Only the distribution of pretest scores must be approximately Normal

How is conditions for 99% CI calculation?

In order to construct a 99% confidence interval for the true mean difference in pretest and posttest scores, we need to meet certain conditions. The only condition that must be met is that the distribution of pretest scores should be approximately Normal. This means that the data collected from the pretest should follow a bell-shaped curve, with the majority of the scores being clustered around the mean. This condition is important because it helps us to make accurate statistical inferences about the population mean difference based on the sample data. The distribution of posttest scores or the difference between posttest and pretest scores are not required to be normal for constructing a confidence interval.

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To construct a 99% confidence interval for the true mean difference in pretest and posttest scores, the condition that must be met is only the distribution of differences (post-pre) must be approximately Normal. Thus, the correct option is D.

When constructing a confidence interval for the true mean difference in pretest and posttest scores, it is only necessary for the distribution of the differences to be approximately Normal. The distributions of the pretest and posttest scores themselves do not need to be Normal, as long as the difference between them is approximately Normal.

However, if all three distributions (pretest, posttest, and the difference) are approximately Normal, this can improve the accuracy and precision of the confidence interval.

Therefore, D is the correct option.

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Answer:

a. \(b=2\)

b. \(b = 2a\)

c. \(a = \frac{1}{2}b\\\)

d. \(b = 10\)

Step-by-step explanation:

Gradient is just another similar term for slope l, \(m\), and it can be calculated by \(m = \frac{y_2 -y_1}{x_2 -x_1}\\\) where \(x_n\) and 1\(y_n\) is the \(xy\)-coordinates of point \(n\)

We let \((0,0)\) be point \(1\) and \((a,b)\) be point \(2\), we can then write the equation:

\(m = \frac{b -0}{a -0}\\ m = \frac{b}{a}\).

It also says that the points are with a gradient of \(2\) so \(m = 2\). We can then write the equation:

\(2 = \frac{b}{a}\\\)

Finding \(b\)If \(a = 1\):

\(2 = \frac{b}{a} \\ 2 = \frac{b}{1} \\ 2 = b \\ b = 2\)

Writing an expression for \(b\) in terms of \(a\).

\(2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{b}{a} \times a = 2 \times a \\ b = 2a\)

Writing an expression for \(a\) in terms of \(b\)

\(2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{a}{b} = \frac{1}{2} \\ \frac{a}{b} \times b = \frac{1}{2} \times b \\ a = \frac{1}{2}b\)

Finding \(b\) if \(a = 5\)

\(2 = \frac{b}{a} \\ 2 = \frac{b}{5} \\ \frac{b}{5} = 2 \\ \frac{b}{5} \times 5 = 2 \times 5 \\ b = 10\)

Answer:

1:2.5

2: 3.5

Step-by-step explanation:

if it is correct then please mark as a brainlist

Answer:

1. 15cm.

2. 27km.

Step-by-step explanation:

This is what I got for the answers, I hope that this helps you.

Answer:

-439° × π / 180°  

= -2.4388888889π rad  

= -7.6619954163 rad

Step-by-step explanation:

π rad = 180°

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Answer:

second option

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

start with 3.46x + 6.38 = -4. Then take away 6.38 from both sides to get 3.46x=-10.38. Then you divide both sides by 3.46 to get x = -3.