Question 3
Write the rational number as a decimal.

Step-by-step explanation:

-5(x + 4)² + 8 = -5(x² + 8x + 16) + 8 =

= -5x² - 40x - 80 + 8 = -5x² - 40x - 72

so, the third answer option must be correct, but you made a mistake there and forgot the "x" as factor of -40.

Answer:

Step-by-step explanation:

Answer:

Y=COS X+1

Step-by-step explanation:

The function whose graph is given by is y = cos x + 1.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of the function y = cos(x) + 1 can be understood by analyzing its two component functions:

cos(x) and 1.

The function cos(x) is a periodic function that oscillates between -1 and 1, with a period of 2π.

The graph of cos(x) is a smooth curve that has its maximum value at x = 0 and its minimum value at x = π (or x = -π).

The function 1 is a constant function that takes on the value of 1 for all values of x.

The graph of 1 is a horizontal line that extends infinitely in both directions along the x-axis.

When we add the two functions together, we get the function:

y = cos(x) + 1.

This function shifts the graph of cos(x) upward by 1 unit, so that it oscillates between 0 and 2, with a maximum value of 2 when cos(x) = 1 and a minimum value of 0 when cos(x) = -1.

The resulting graph of y = cos(x) + 1 is a periodic curve that oscillates above and below the horizontal line y = 1, with a period of 2π.

It has its maximum value of 2 when x = 2nπ (where n is an integer), and its minimum value of 0 when x = (2n + 1)π (where n is an integer). The graph is symmetric about the line y = 1, which is the horizontal asymptote of the function.

Thus,

The function whose graph is given by is y = cos x + 1.

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Answer:

y = x + 2

Step-by-step explanation:

We start by writing the coordinates pair

(x, f(x))

So we have;

(5,7) and (-2,0)

We start by getting the slope;

m = y2-y1/x2-x1

m = 0-7/-2-5 = -7/-7 = 1

The equation of a linear equation has the general form;

y = mx + c

m is the slope and c is the y-intercept

y = x + c

to get the value of c, we make a simple substitution

we can use the x and y values of any point

7 = 5 + c

c = 7-5

c = 2

So the equation is;

y = x + 2

Answer:

The value of y is 12

Step-by-step explanation:

-5(2y – 15) + 4y = 3

-10y + 75 + 4y = 3

-10y + 4y + 75 - 75 = 3 - 75

-6y = -72

Take negative sign ( – ) Common

6y = 72

Now, Divide both side by 6 we get,

6y/6 = 72/6

y = 12

Thus, The value of y is 12

-TheUnknownScientist 72

Solutions for the given graph can be be given as function  \($ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.\)

A relation called a "function" is one in which each input has just one Solution.

In the relationship, y is a function of x because there is only one solution y for each input x (1, 2, 3, or 0). Since y = 3 has multiple solution (x = 1 and x = 2), x is not a function of y.

As we can see, f(x) has two inequalities

in first case x ≤ -1.5

And equation is

\($m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

m = -2

Line equation

y - 0 =  -2(x - (-1.5))

y = −2x − 3

in second case x ≤ -1.5

And equation is

\($m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

m = 0.75

Line equation

y - 0 =  0.75(x - (-4))

y = 0.75x + 3

\($ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.\)

Thus, Solutions for the given graph can be be given as function  \($ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.\)

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By the compare to y =mx + b, the value of slope (m) is 1/10 and value of y - intercept is 0.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The expression is,

⇒ v = 1/10u

Now, We can write as;

⇒ v = 1/10u

⇒ v = 1/10u + 0

By compare with y = mx + b, we get;

⇒ slope (m) = 1/10

⇒ y - intercept (b) = 0

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Answer:

Rounded=37.7

Step-by-step explanation:

C=2πr=2·π·6≈37.69911

Based on the sample data and the hypothesis test, Bill McWaffle should not take a public position on the issue of gambling legalization.

Using the normal approximation, we can calculate the test statistic, which follows a standard normal distribution under the null hypothesis. The test statistic is given by:

Z = (p - p₀) / √(p₀(1 - p₀) / n),

where p₀ represents the proportion specified under the null hypothesis, which is 0.65 in this case.

Substituting the values into the formula, we have:

Z = (0.34 - 0.65) / √(0.65(1 - 0.65) / 200) ≈ -9.91.

Looking up the z-value in a standard normal distribution table or using statistical software, we find that the critical value for a one-sided 99 percent confidence level is approximately 2.33.

Since the test statistic (Z = -9.91) is much smaller (in absolute value) than the critical value (2.33), we have strong evidence to reject the null hypothesis. This means that the proportion of constituents in favor of legalization is significantly less than 65 percent.

This decision ensures that he does not risk alienating a large segment of voters, as the data does not provide sufficient evidence to support a clear majority opinion of at least 65 percent in favor of legalization.

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Answer: To check a solution, you can substitute the solutions into the equations and verify that both equations are true.

Step-by-step explanation:

The task is to find the probability of a bulb lasting for at least 545 hours given that the variance of the lifetime is 225 and the mean lifetime is 570 hours.

Since the lifetime of light bulbs is normally distributed, we can use the properties of the normal distribution to calculate the probability. In this case, we know the mean (570 hours) and the variance (225).

To find the probability of a bulb lasting for at least 545 hours, we need to calculate the area under the normal curve to the right of 545 hours.

First, we standardize the value of 545 using the formula: z = (x - μ) / σ

Where x is the value (545 hours), μ is the mean (570 hours), and σ is the standard deviation (square root of the variance, which is 15 in this case).

Next, we use a standard normal distribution table or a statistical calculator to find the cumulative probability corresponding to the standardized value. The cumulative probability represents the area under the normal curve to the left of the standardized value.

Finally, we subtract the cumulative probability from 1 to get the probability of a bulb lasting for at least 545 hours. The resulting probability can be rounded to four decimal places.

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The null hypothesis of this study is the statement that there is no significant difference between the playfulness of cats and dogs with their owners. In other words, the researcher assumes that both cats and dogs will play with their owners at the same rate. This is option c.

To test this hypothesis, the researcher would need to collect data on the playfulness of both cats and dogs with their owners. This could involve observing the animals during playtime or asking owners to self-report how often their pets play with them. The data would then be analyzed using statistical tests to determine if there is a significant difference in the average rates of playfulness between cats and dogs.

It is important to note that the null hypothesis does not necessarily reflect the researcher's personal beliefs or assumptions about the topic. Instead, it serves as a baseline assumption that can be tested through empirical research. If the data collected suggests that cats and dogs do not play with their owners at the same rate, then the null hypothesis would be rejected, and the researcher would need to explore alternative explanations for the observed differences.

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If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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The other side length is √20 after applying the Pythagoras and other two sides are 2 and 2√3.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

One side length = 2

Other side length = 2√3

Apply Pythagoras

x^2 = 2^2 + (2√3)^2

x^2 = 4 + 12

x = √20

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If three pencils, each measuring one foot in length, are laid end to end touching, the total distance covered by the row would be 3 feet.

Since each pencil is 1 foot long, when three pencils are laid end to end, they form a row that is 3 feet long. The key information here is that the pencils are touching, which means there are no gaps between them. Therefore, the row would extend for a total distance of 3 feet.

In this scenario, the correct answer is option a, 3 ft. The row would not extend beyond 3 feet because there are only three pencils, each measuring one foot in length. If there were more pencils or if they were not touching end to end, the total distance covered by the row would be different. However, based on the given information, the row formed by the three one-foot-long pencils would have a length of 3 feet.

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Answer:

It is so multiple 2y-4y and u will get ur answer

the distance between two points is 3.5 cm

The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.

(1,-2) (1,1.5)

distance between two points is

= \(\sqrt{(1-1)^{2} + (1.5+2)^{2}\)

= 3.5 cm

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Answer:

1. y = 4x - 2

2. y = \(\frac{1}{3}\)x + 4

3. y = -x

Step-by-step explanation:

use the \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\) to find the gradient

and input one of the points to get the y-intercept.

Answer:

y = 0

Step-by-step explanation:

x + 2y = 2 ( subtract 2y from both sides )

x = 2 - 2y → (1)

x = - 4y + 2 → (2)

substitute x = 2 - 2y into (2)

2 - 2y = - 4y + 2 ( add 4y to both sides )

2 + 2y = 2 ( subtract 2 from both sides )

2y = 0 , then

y = 0

The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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The probability that exactly 7 rivets fail the test is approximately 0.0483.

To calculate this probability, we first define p as the probability that a rivet will hold a 200 lb. force without any deformation. Thus, the probability of a rivet failing to hold a 200 lb. force is 1 - p. In this case, p is given as 0.99, so the probability of a rivet failing is 0.01.

Next, we let X represent the number of rivets that fail the test. Since the number of rivets tested is 500, we can model X as a binomial random variable with parameters n = 500 (the number of trials) and p = 0.01 (the probability of failure).

We want to find the probability that exactly 7 rivets fail the test, which can be denoted as P(X = 7).

This probability can be calculated using the binomial probability formula:

P(X = 7) = (500C7) * (0.01^7) * (0.99^(500-7))

Here, (500C7) represents the number of ways to choose 7 rivets out of 500, which is calculated as 500! / (7! * (500-7)!).

Evaluating this expression, we find that P(X = 7) is approximately 0.0483.

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100 grams i think? not entirely sure

Answer: 600 grams

Step-by-step explanation:

Mass does not change with gravity. Weight changes with gravity

The sum of all repetitions performed multiplied by the resistances used during a strength-training session is the workload.

To find the sum of all repetitions performed multiplied by the resistances used during a strength-training session, you would need to calculate the total workload.

This can be done by multiplying the number of repetitions for each exercise by the resistance used for that exercise, and then adding up the results for all exercises performed during the session.

For example, if you did 10 reps of bench press with 100 pounds, 8 reps of bicep curls with 50 pounds, and 12 reps of squats with 150 pounds, the total workload would be (10 x 100) + (8 x 50) + (12 x 150) = 2,600 pounds. This number represents the total amount of weight lifted during the session and can be used to track progress and adjust future workouts.

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Plot point F where angle alpha is located.

Triangle ABF has two interior angles x and 80. They add to the exterior angle alpha due to the remote interior angle theorem.

alpha = x+80

The diagonal measurement as √5625 ft, which is approximately 75 feet, the correct answer is B. 75 ft 0 in.

The diagonal measurement of the rectangular slab on grade can be found using the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the length and width of the slab.

To calculate the diagonal measurement, we can apply the Pythagorean theorem:

Diagonal² = Length² + Width²

Substituting the given values, we have:

Diagonal² = (60 ft 0 in.)² + (45 ft 0 in.)²

Calculating this expression, we find:

Diagonal² = 3600 ft² + 2025 ft²

Diagonal² = 5625 ft²

Taking the square root of both sides, we obtain:

Diagonal = √5625 ft

Diagonal ≈ 75 ft

Therefore, the diagonal measurement of the rectangular slab on grade is approximately 75 feet.

To find the diagonal measurement of the rectangular slab on grade, we can use the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width).

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Answer:

C. y = - 0.5 (x - 6)² + 18

Step-by-step explanation:

Because it is "Correct Answer"

Answer:

1530

Step-by-step explanation:

Answer: 1, 530

Step-by-step explanation:

The singular value decomposition is a factorization of a matrix into three separate matrices. It has many applications in various fields, including data compression, image processing, and machine learning.

To find the singular value decomposition (SVD) of the given matrix, let's go through the steps:

1. Begin with the given matrix:
  1 1
  -1 1
  -1 1

2. Calculate the transpose of the matrix by interchanging rows with columns:
  1 -1 -1
  1 1 1

3. Multiply the matrix by its transpose:
  1 -1 -1    1
  1 1 1      1
  -1 1 1     -1

4. Calculate the eigenvalues and eigenvectors of the resulting matrix. This step involves finding the values λ that satisfy the equation A * v = λ * v, where A is the matrix.

5. Normalize the eigenvectors obtained in step 4 to obtain orthonormal eigenvectors.

6. The singular values are the square roots of the eigenvalues.

7. Create the matrix U by taking the orthonormal eigenvectors obtained in step 5 as columns.

8. Create the matrix Σ by arranging the singular values obtained in step 6 in a diagonal matrix.

9. Create the matrix V by taking the normalized eigenvectors obtained in step 5 as columns.

10. Finally, write the answer in the form of SVD: A = U * Σ * \(V^T\), where U, Σ, and \(V^T\) represent the matrices from steps 7, 8, and 9 respectively.

To find the singular value decomposition (SVD) of a matrix, we need to perform several steps. These include finding the eigenvalues and eigenvectors of the matrix, normalizing the eigenvectors, calculating the singular values, and creating the matrices U, Σ, and V. The SVD provides a way to factorize a matrix into three separate matrices and has many practical applications.

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