On a coordinate plane, rectangle 1 has points (1, negative 2), (4, negative 2), (4, negative 3), (1, negative 3). Rectangle 2 has points (negative 3, negative 1), (negative 2, negative 1), (negative 2, negative 4), (negative 3, negative 4).
Rectangle 2 is the image of rectangle 1 after it rotates
degrees clockwise.

Answer: X = 5.0

Step-by-step explanation:

- since these are right triangles you can use trigonometry to solve this pretty easily

- for this situation, you only have to use sine/sin

__________________________________________________________

- to start you just need to identify which side is which:

- so, for this problem the equation is: \(10xSin(45) = 7.071067812\)

__________________________________________________________

- so 7.071067812 is the hypotenuse of the smaller triangle so you just do the same thing again

- start with identifying which side is which:

- so for this part, the equation is: \(7.071067812xSin(45) = 5.0\)

- so X = 5.0

__________________________________________________________

hope this helps :)

Answer:

x = 5

Step-by-step explanation:

Check the file for detailed solution.

This involves SOH-CAH-TOA method, always remember that the opposite of the 90 degree mark is always the hypotenuse. Meanwhile, the position of the given angle (theta) is dependent on which side it is placed. It give either an adjacent or opposite side.

Answer:

I shall help you again the answer is 1/4

Step-by-step explanation:

Use photo math it's useful no need to Say thanks

The unknown measures in the triangle are:
Side b ≈ 6.9
Side c ≈ 9.2
Angle A ≈ 55 degrees

To find all unknown measures in the triangle, we need to use the properties of triangles and trigonometry. Let's label the angles and sides of the triangle as follows:

Angle A is opposite side a
Angle B is opposite side b
Angle C is opposite side c

Using the Law of Sines, we can find one of the unknown sides, let's say side c:

c/sin(C) = a/sin(A)

Plugging in the given values:

c/sin(65) = 8/sin(55)

Solving for c:

c = 8(sin(65)/sin(55)) ≈ 9.2

Next, we can use the Law of Cosines to find another unknown side, let's say side b:

b² = a² + c² - 2ac*cos(B)

Plugging in the known values:

b² = 8² + 9.2² - 2(8)(9.2)*cos(60)

Solving for b:

b ≈ 6.9

Finally, we can find the remaining angle, angle A, using the fact that the angles in a triangle add up to 180 degrees:

A = 180 - B - C = 180 - 60 - 65 = 55

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The total number of different choices for the representative is 114

The number of choices for the representative to the university committee is the sum of the number of CS faculty members and the number of CS majors who are not faculty members.

Since no one can be both a faculty member and a student.

The number of choices for a faculty member is simply the number of members of the CS faculty, which is 9.

The number of choices for a CS major who is not a faculty member can be calculated by subtracting the number of CS faculty members from the total number of CS majors: 114 - 9 = 105.

Therefore, the total number of different choices for the representative is:

9 + 105 = 114

So there are 114 different choices for the representative to the university committee.

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The intersection of sets a and b has 4 elements.

The intersection of sets is a set that contains the common elements of both sets.

The number of elements in the intersection of A and B is obtained according to the rule presented as follows:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

We have the following information:

n(a ∪ b) = 60 elements

n(a) = 24 elements

n(b) = 40 elements

We can use the formula for the number of elements in the union of two sets to find the number of elements in the intersection of the two sets.

n(a ∪ b) = n(a) + n(b) - n(a ∩ b)

       60 = 24 + 40 - n(a ∩ b)

       60 = 64 - n(a ∩ b)

n(a ∩ b) = 64 - 60

             = 4

So, the intersection of sets a and b has 4 elements.

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The general equation of an ellipse in which case it is not centered at the origin and it is tilted is; (x-h)²/a² + (y-k)²/b² = 1.

It follows from the task content that the plane shape in discuss is an ellipse which is described by the characteristics that it is tilted and not centered at the origin.

It follows from convention that the general equation of such an ellipse is;

(x-h)²/a² + (y-k)²/b² = 1.

In which case, such an ellipse has center given as point; (h, k).

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The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

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Answer:

D

Step-by-step explanation:

everything that should happen at x+4 happens now at x. that is what that means.

so, the graph shifts 4 units to the left.

Answer:

Think it would be 7(c+2)=4

The straight line distance from the airplane to the observer is 476. 70 feet

Note that there are six different trigonometric identities in mathematics, they are;

From the diagram shown, we have that;

Opposite side = 400 feet

Angle of elevation, θ = 40 degrees

Adjacent side = distance

Using the tangent identity, we have;

tan 40 = 400/x

x = 400/0.8391

x = 476. 7 feet

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Answer:

B

Step-by-step explanation:

Let's denote the unknown number as 'x'. The equation can be set up as x + (1/2)x = 45. Solving this equation, we find that the number is 30.

The problem states that the sum of a number and its half is equal to 45. To find the number, we can set up an equation and solve for it.

Let's represent the number as "x". The problem states that the sum of the number and its half is equal to 45. Mathematically, this can be written as:

x + (1/2)x = 45

To simplify the equation, we can combine the like terms:

(3/2)x = 45

To isolate the variable x, we can multiply both sides of the equation by the reciprocal of (3/2), which is (2/3):

x = 45 * (2/3)

Simplifying the right side of the equation:

x = 30

Therefore, the number is 30.

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Two numbers whose product is 1 are called multiplicative inverses or reciprocals.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Given that,

There are two numbers whose product is 1.

Let the two numbers are a and b.

Since, the product of numbers is 1, implies that,

Both the numbers are multiplicative inverse or reciprocal to each others,

Implies that,

a = 1/b

So, the numbers are in the form of 1/b and b.

Hence, both the numbers are reciprocals to each other.

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Two numbers whose product is 1 are called the multiplicative inverse of a number or its reciprocal.

Lets the two number are x and  \(\dfrac{1}{x}\). Then  \(\dfrac{1}{x}\) Is a multiplicative inverse or reciprocal  of x. Since when we multiply both the numbers we get their product is 1.

Hence, for any non-zero number "x" its multiplicative inverse is denoted as \(\dfrac{1}{x}\).

We can say, if two numbers x and \(\dfrac{1}{x}\) Satisfies the equation \(x\times\dfrac{1}{x}=1\) Then they are reciprocals or multiplicative inverses of each others.

0 has no reciprocal, since when any number is multiplied with 0 it will always result in 0  not 1.

Hence, the answer is: Two numbers whose product is 1 are called or reciprocals.

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Answer:

Question 1

Ordered pair (2, -3) satisfies y ≥ x - 5 but does not satisfy y ≤ 2x-8

Question 2

Ordered pair (0,4) does satisfy both inequalities:
y ≤ -x + 4 and y ≥ 5x - 3

Step-by-step explanation:

Question 1

The ordered pair is (2, -3); therefore x = 2, y = -3

Plug these values into the left and right side of each inequality and see if these values satisfy the inequality

For y ≥ x - 5
LHS = -3, RHS = 2 - 5 = -3

Is -3 ≥ -3? Of course; in fact it is = and it only need to satisfy either = or >

For y ≤ 2x-8
LHS = -3, RHS = 2(2) - 8 = 4 - 8 = -4

Is -3 ≤ -4? NO. -3 is greater than -4
(remember in negative  numbers -4 lies further to the left than -3 on the number line so -4 is less than -3)

Question 2

Given ordered pair is (0,4)

For y ≤ -x + 4

LHS = 4, RHS = -0 + 4 = 4

Is 4 ≤ 4? YES

For y ≥ 5x -3

LHS = 4, RHS = 5(0) -3 = 0 - 3 = -3

Is 4 ≥ -3? Of course. All positive numbers are greater than negative numbers

In this case, since we want the sample mean to be within 0.01 of the population mean, the margin of error is 0.01.

To determine the number of grade-point averages needed to have a sample mean within 0.01 of the population mean, we can use the formula for the margin of error. The margin of error is calculated by dividing the standard deviation of the population by the square root of the sample size, multiplied by a constant value.

To find the required sample size, we need to know the standard deviation of the population. However, since it is not provided, we cannot calculate the exact number of grade-point averages needed.
If you have the standard deviation of the population, you can use the following formula to calculate the sample size:
Sample size = (Z * standard deviation) / margin of error

Where Z is the constant value that corresponds to the desired level of confidence. For example, if you want a 95% confidence level, Z would be approximately 1.96.

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Answer:

Step-by-step explanation:

Let the number be x

The we have below equation to solve for x:

Answer:

(5,3)

Step-by-step explanation:

Sharon, an 8th grader, found the following values for weekly allowances in dollars of seven of her friends: 5, 7, 10, 8, 6, 12, and 15. if Sharon wanted to construct a one-sample t-statistic, the number of degrees of freedom is

6 degrees of freedom

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom.

When calculating degrees of freedom, one is subtracted from the total number of items in the data sample.

mathematically, for number of data, n

degree of freedom = n - 1

the given problem has n = 7

degree of freedom = 7 - 1

degree of freedom = 6

the number of degree of freedom is 6

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Answer:

115 persons in a population of 4,399 became ill with a disease of unknown etiology. The 115 cases occurred in 77 households.

Step-by-step explanation:

Answer is h(x) =\(\frac{1}{2}\) cos (\(\frac{2}{3}\)π +\(\frac{2}{3}\)π ) - \(\frac{1}{2}\)

∵The maximum point (- 2π. 3 )

        minimum point (- π / 2 , - 4)

and h(x) = a cos (b x + c)+ d

∴ a + d = 3                                d = - 1/ 2

                                  ⇒  

 -a + d = -4                              a = 7 / 2

{solve the equation}

and   -2πb + c = 0                      b = 2 / 3

                                       ⇒

       - ( π/ 2) b + c =  λ              c = 4 / 3 π

∴ h(x) =\(\frac{1}{2}\) cos (\(\frac{2}{3}\)π +\(\frac{2}{3}\)π) - \(\frac{1}{2}\)

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant

here detail explanation:

Sine Function

Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:

Sin a =Opposite/Hypotenuse = CB/CA

Cos Function

Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.

Cos a = Adjacent/Hypotenuse = AB/CA

Tan Function

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.

Tan a = Opposite/Adjacent = CB/BA

Also, in terms of sine and cos, tan can be represented as:

Tan a = sin a/cos a

Secant, Cosecant and Cotangent Functions

Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:

Sec a = 1/(cos a) =  Hypotenuse/Adjacent = CA/AB

Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB

cot a = 1/(tan a) = Adjacent/Opposite = BA/CB

Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.

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Luke's jump rope is greater than cooper's when the given mixed fraction was converted to an improper fraction and then a decimal by 0.35m.

What are mixed fractions?

Converting each mixed fraction to an improper fraction and then decimal to compare between two values, we get-

Cooper's jump rope length= \(4\frac{2}{5}\) = 22/5 =4.4 m

Luke's jump rope length = \(4\frac{3}{4}\) = 19/4 = 4.75 m

Luke's jump rope is greater than cooper's by 4.75-4.4 =0.35m

Comparing both lengths, we get that Luke's jump rope is greater than cooper's when the given mixed fraction was converted to an improper fraction and then a decimal by 0.35m.

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The approximate change in z for the given change in the independent variables is 0.61.

To approximate the change in z for the given change in the independent variables, we can use differentials. The differential of z can be expressed as:

dz = (∂z/∂x)dx + (∂z/∂y)dy

First, let's find the partial derivatives (∂z/∂x) and (∂z/∂y) by taking the partial derivatives of the function z = x^2 - 7xy with respect to x and y, respectively.

∂z/∂x = 2x - 7y
∂z/∂y = -7x

Next, we'll substitute the values of x, y, dx, and dy into the differentials equation. Given that (x, y) changes from (5, 3) to (5.04, 2.97), we have:
x = 5
y = 3
dx = 0.04
dy = -0.03

Substituting these values into the equation dz = (∂z/∂x)dx + (∂z/∂y)dy, we get:

dz = (2(5) - 7(3))(0.04) + (-7(5))( -0.03)
= (10 - 21)(0.04) + (-35)( -0.03)
= (-11)(0.04) + (1.05)
= -0.44 + 1.05
= 0.61

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Answer:

5.59 times per second.

Step-by-step explanation:

Direct variation is in the form:

\(y=kx\)

Where k is the constant of variation.

Inverse variation is in the form:

\(\displaystyle y=\frac{k}{x}\)

In the given problem, the frequency of a vibrating guitar string varies inversely  as its length. In other words, using f for frequency and l for length:

\(\displaystyle f=\frac{k}{\ell}\)

We can solve for the constant of variation. We know that the frequency f is 4.3 when the length is 0.65 meters long. Thus:

\(\displaystyle 4.3=\frac{k}{0.65}\)

Solve for k:

\(k=4.3(0.65)=2.795\)

So, our equation becomes:

\(\displaystyle f=\frac{2.795}{\ell}\)

Then when the length is 0.5 meters, the frequency will be:

\(\displaystyle f=\frac{2.795}{.5}=5.59\text{ times per second.}\)

Answer:

; (1.8 meters per minute)

Step-by-step explanation:

Use dimensional analysis to solve this problem.

The proper units of conversion are given in parentheses on this question: 100 cm = 1 m.

Start with the given value, 3 centimeters/1 second.

Convert this rate to meters/minute by multiplying 3 cm/1 sec by 1 m/100 cm.

The top and bottom units should cancel out, so that's how you know to put the cm units on the bottom to cancel out with the 3 cm on the top.

Multiply the fractions together. The "cm" units cancel out.

Now you want to make the bottom units = minutes. There are 60 seconds in 1 minute, so you can use  to multiply with .

The "seconds" unit cancels out, so you are left with meters on the top and minutes on the bottom. Multiply the fractions together.

We want the rate to be meters per minute (1), so completely simplify this fraction and divide the fraction by (100/100), so the denominator is 1 min.

Step-by-step explanation:

The probability that a randomly picked fruit will weigh between 362.8 grams and 374.9 grams can be calculated using the standard normal distribution and the z-score formula .

To find the probability, we need to calculate the z-scores for the lower and upper bounds. The z-score is given by (X - μ) / σ, where X is the value, μ is the population mean, and σ is the population standard deviation.

For the lower bound, the z-score is (362.8 - 376) / 11 ≈ -1.2, and for the upper bound, the z-score is (374.9 - 376) / 11 ≈ -0.1091. Using a standard normal table or calculator, we can find the corresponding probabilities for these z-scores.

The probability corresponding to the lower z-score is approximately 0.1151, and the probability corresponding to the upper z-score is approximately 0.4573. To find the probability within the range, we subtract the lower probability from the upper probability:

0.4573 - 0.1151 = 0.3422. Therefore, the probability that a randomly picked fruit will weigh between 362.8 grams and 374.9 grams is approximately 0.3422, or 34.22%.

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Answer:

C = K − 273.15  !!!!!

Yes, Its the equation, since we do not have either varibles it is written out like so

Step-by-step explanation:

By simplifying both sides of the equation, then isolating the variable.

\(3\) and \(116^{\circ}\) are supplementary angles.

Therefore

\(m\angle 3+116^{\circ}=180^{\circ}\\m\angle 3=64^{\circ}\\\)