Winston drew a scale drawing of the elementary school. He used the scale 8 centimeters=10 meters. What is the scale factor of the drawing?

Answer:

(-5, 5)

Step-by-step explanation:

A graph exists only for (-5, 5).  This is the domain.

Answer: 1.118

Step-by-step explanation:

Factor x Factor = Product

0.26(Factor) x 4.3(Factor) = 1.118(Product)

To check your work, divide the product by one of the factors and the result you should get is the other factor.

1.118(Product) ÷ 4.3(Factor) = 0.26(Factor)

-or-

1.118(Product) ÷ 0.26(Factor) = 4.3(Factor)

To show work:

     .26

   x4.3

   .078

+1.040

  1.118

Main Answer:The correct answer is "equality of three or more population means."

Supporting Question and Answer:

What is the purpose of the one-way analysis of variance (ANOVA) test?

ANOVA helps to assess whether these differences are statistically significant by comparing the variation between the groups to the variation within the groups.

Body of the Solution:The one-way analysis of variance (ANOVA) is used to test for" the equality of three or more population means". ANOVA compares the variation between the groups (due to differences in means) to the variation within the groups (due to individual differences within each group) to assess whether the observed differences in means are statistically significant. Therefore, the correct answer is:

"equality of three or more population means."

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Note that the  the quotient of the expression is 7a³  + a²b - 3.

The expression can be written this way

(28a⁴ᵃᵇ + 4a²b² - 12ab) / (4ab)

To simplify the expression, we can cancel out common factors in the numerator and denominator.

In this case, we can divide every term by 4ab:

(28a⁴ᵃᵇ / 4ab) + ( 4a²b² / 4ab) - (12ab / 4ab)

Simplifying further, we have:

7a³ + a²b - 3

Thus, we can state that , the quotient of the expression is 7a³ + a²b - 3

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To construct a matrix with the required property (a), (d) & (e) are possible to construct the matrix. (b), (c) are not possible to construct the matrix.

(a) It is possible to construct a matrix with the given properties as follows:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\). The columns of this matrix span the column space, and the vector (-1,0,1) spans the nullspace.

(b) It is not possible to construct a matrix with the given properties because the dimensions of the column space and the nullspace are different. The column space is a subspace of \(R^3\), whereas the nullspace is a subspace of\(R^1\).

(c) It is not possible to construct a matrix with the given properties because the dimensions of the column space and the left nullspace are different. The column space is a subspace of\(R^3\), whereas the left nullspace is a subspace of \(R^2\).

(d) It is possible to construct a matrix with the given properties as follows:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\). The rows of this matrix span the row space, and the vector (1,0,3,2) spans the nullspace.

(e) It is possible to construct a matrix with the given properties as follows:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\). The rows of this matrix span the row space, and the vector (-3,1) spans the left nullspace.

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Therefore, you have 25 dogs at the shelter.

Answer:

25

Step-by-step explanation:

We can take our ratio of 3:5 and multiply it by 5 to give us the number of cats we have. We get 15:25. Meaning we have 25 dogs.

Answer:

x= -3

y= 1

Step-by-step explanation:

y=4x+13

y=6x+19

put them equal to each other

4x+13=6x+19

subtract 4x from each side

13=2x+19

subtract 19 from both sides

-6 = 2x

divide by 2

x= -3

plug x into one of the equations

y=4x+13

y=4(-3)+13

y= -12+13

y= 1

Answer:

532.12

Step-by-step explanation:

251 x 2 = 502

502 x .06 = 30.12

30.12 + 502 = 532.12

Her regular fare will be $15.06.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The $251 includes a 6% tax on the regular fare.

Now,

Since, The $251 includes a 6% tax on the regular fare.

Hence, The regular fare = 6% of $251

                                      = 6/100 × 251

                                      = $15.06

Thus, Her regular fare will be $15.06.

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Answer:

see explanation

Step-by-step explanation:

(h + k)(x) = h(x) + k(x), thus

h(x) + k(x)

= x² + 1 + x - 2 = x² + x - 1 , then

(h + k)(2) = 2² + 2 - 1 = 4 + 2 - 1 = 5

----------------------------------------------------

(h - k)(x) = h(x) - k(x), thus

h(x) - k(x)

= x² + 1 - (x - 2) = x² + 1 - x + 2 = x² - x + 3, then

(h - k)(3) = 3² - 3 + 3 = 9 - 3 + 3 = 9

-----------------------------------------------------

h(2) = 2² + 1 = 4 + 1 = 5

k(3) = 3 - 2 = 1

Thus

3h(2) + 2k(3)

= 3(5) + 2(1) = 15 + 2 = 17

The answers shown is below

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.

h(x) + k(x)

= x² + 1 + x - 2

= x² + x - 1

(h + k)(2)

= 2² + 2 - 1

= 4 + 2 - 1

= 5

h(x) - k(x)

= x² + 1 - (x - 2)

= x² + 1 - x + 2

= x² - x + 3

(h - k)(3)

= 3² - 3 + 3

= 9

k(3) = 3 - 2 = 1

3h(2) + 2k(3)

= 3(5) + 2(1)

= 15 + 2

= 17

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The correct answer is Probability and non probability sampling procedure.

There are two distinct exits from sampling procedures.

There are two types of sampling: probability sampling and non-probability sampling.

In probability sampling each population has equal and independent chance to comes in the study . There are various types of probability samplings technique exists . These are simple random sampling , stratified random sampling, cluster sampling , systematic random sampling etc.

In non probability sampling the samples are selected on the basis of personal biasness, judgments and preferences. Judgemental sampling , quota sampling, dimensional sampling etc comes under this type of sampling procedure.

So here the correct answer is

Option -E- Probability and non probability sampling procedure.

Except it all other options are wrong.

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The equation of the parabola is y = 2(x - 1)² + 3

From the question, we have the following parameters that can be used in our computation:

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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0 ≤ x < 2, where x is an integer. Option C

The appropriate domain for the function f(x) = 42 - 15x in the given context can be determined by considering the constraints of the problem.

Tyson has a $50 gift card, and he wants to purchase a belt that costs $8 and x number of shirts that cost $15 each. The function f(x) represents the balance on the gift card after Tyson makes the purchases.

The number of shirts Tyson can purchase depends on the remaining balance on the gift card. Since each shirt costs $15, the maximum number of shirts he can buy is limited by the amount of money left on the gift card.

If we subtract the cost of the belt ($8) and the cost of x shirts ($15x) from the initial balance ($50), we should get a non-negative result, indicating that Tyson has enough money on the gift card to make the purchases.

Therefore, we can set up the inequality:

50 - 8 - 15x ≥ 0

Simplifying, we have:

42 - 15x ≥ 0

Now, we can solve for x:

-15x ≥ -42

Dividing by -15 (remembering to flip the inequality sign), we get:

x ≤ 42/15

x ≤ 2.8

Since x represents the number of shirts Tyson can buy, it should be a whole number. Therefore, the appropriate domain for the function f(x) is:

0 ≤ x ≤ 2, where x is an integer.

Option C.

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The side length of the square is 2/3 foot.

A number system is defined as a system of writing to express numbers.

To find the side length of a square, we can take the square root of its area.

Given that the area of the square is 16/36 square foot

we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 4:

16/36  

=(16 ÷ 4) / (36 ÷ 4)

= 4/9 square foot.

Taking the square root of 4/9 gives us the side length of the square:

√(4/9) = 2/3 foot.

Therefore, the side length of the square is 2/3 foot.

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The Values of p, c, and d are -1, 3, and -1, respectively.

(a) We are given that the coordinates of the turning points on the graph of \(y=f(x)\) are (-1, 5) and (u, v). Let's start by substituting the given values into the equation \(f(x) = x^3 - 3x^2 + cx + d\) to find the values of c, d, and v.

For the turning point (-1, 5), we have:

\[f(-1) = (-1)^3 - 3(-1)^2 + c(-1) + d = -1 + 3 + (-c) + d = 5\]

Simplifying, we get:

\[4 - c + d = 5 \Rightarrow -c + d = 1 \quad \text{(1)}\]

For the turning point (u, v), we have:

\[f(u) = u^3 - 3u^2 + cu + d = v\]

Substituting the values of u and v, we get:

\[u^3 - 3u^2 + cu + d = v\]

Now, let's substitute the values of c, d, and v from equation (1) into the above equation:

\[u^3 - 3u^2 - u + 1 = 0\]

We can observe that this equation is satisfied when u = 1. Therefore, we have found that c = -9, d = 0, and v = -27. Also, the value of u is 1.

(b) To find the values of d for which the graph of \(y = x^3 - 3x^2 - 9x + d\) crosses the x-axis at three distinct points, we need to determine the conditions for the cubic equation to have three real roots. For a cubic equation in the form \(ax^3 + bx^2 + cx + d = 0\), if the discriminant \(\Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2\) is positive, then the equation has three distinct real roots.

In this case, we have \(a = 1\), \(b = -3\), \(c = -9\), and the discriminant \(\Delta = -2916d + 108c^3 + 4b^3d - 27a^2d^2 + b^2c^2\).

By substituting the values of c = -9 and b = -3 into the discriminant expression, we have:

\[\Delta = -2916d + 108(-9)^3 + 4(-3)^3d - 27(1)^2d^2 + (-3)^2(-9)^2\]

Simplifying further:

\[\Delta = -2916d - 8748 + 108d - 27d^2 + 243\]

\[\Delta = -27d^2 - 2812d - 8505\]

For the equation to have three distinct real roots, \(\Delta\) must be positive. So we solve the inequality:

\[-27d^2 - 2812d - 8505 > 0\]

Using quadratic techniques, we can find the range of values for d that satisfy the inequality.

(c) To find the values of c and d for which the graph of \(y = x^3 - 3x^2 + cx + d\) has two distinct turning points, we need to determine the conditions for the cubic equation to have two real roots. For a cubic equation in the

form \(ax^3 + bx^2 + cx + d = 0\), if the discriminant \(\Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2\) is positive and the sign of \(f''(x)\) changes, then the equation has two distinct turning points.

In this case, we have \(a = 1\), \(b = -3\), and the discriminant \(\Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2\).

By substituting the values of a = 1 and b = -3 into the discriminant expression, we have:

\[\Delta = 18cd - 4(-3)^3d + (-3)^2c^2 - 4c^3 - 27d^2\]

Simplifying further:

\[\Delta = 18cd + 36d - 9c^2 - 4c^3 - 27d^2\]

To determine the values of c and d for which \(\Delta\) is positive and the sign of \(f''(x)\) changes, we need to analyze the nature of the graph and the second derivative of the cubic function \(f(x)\). However, without specific information about the behavior of the function, we cannot determine the precise values of c and d that satisfy these conditions.

(d) If the graph of \(y = f(x)\) is translated p units to the left away from the y-axis, it becomes the graph of \(y = x^3\). To determine the values of p, c, and d in this case, we need to compare the equations of the two functions and observe the effect of the translation.

Comparing the equations, we have:

\[f(x) = x^3 - 3x^2 + cx + d\]

\[y = x^3\]

To translate the graph of \(f(x)\) p units to the left, we replace \(x\) with \(x + p\) in the equation. So we have:

\[y = (x + p)^3\]

Comparing this equation with the original equation, we can equate the terms to find the values of p, c, and d:

\[x^3 - 3x^2 + cx + d = (x + p)^3\]

Expanding the right side using binomial expansion, we get:

\[x^3 - 3x^2 + cx + d = x^3 + 3px^2 + 3p^2x + p^3\]

Comparing the coefficients of like terms, we have:

\[3p = -3 \quad \Rightarrow \quad p = -1\]

\[3p^2 = c \quad \Rightarrow \quad c = 3\]

\[p^3 = d \quad \Rightarrow \quad d = -1\]

Therefore, in this case, the values of p, c, and d are -1, 3, and -1, respectively.

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The probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.

i) To find the probability that the word starts with M, we need to consider the total number of possible arrangements of the letters and the number of arrangements that start with M. The word "MOBILE" has 6 letters, so there are 6! = 720 possible arrangements of the letters. To find the number of arrangements that start with M, we can fix the M in the first position and arrange the remaining 5 letters in the remaining positions, which gives us 5! = 120 arrangements. Therefore, the probability that the word starts with M is:

P(starts with M) = number of arrangements that start with M / total number of arrangements

= 120 / 720

= 1/6

ii) To find the probability that the word starts with M and ends with E, we can fix the M in the first position and the E in the last position, and then arrange the remaining 4 letters in the remaining positions. This gives us 4! = 24 arrangements. Therefore, the probability that the word starts with M and ends with E is:

P(starts with M and ends with E) = number of arrangements that start with M and end with E / total number of arrangements

= 24 / 720

= 1/30

Thus, the probability that the word so formed starts with M is 1/6, and the probability that it starts with M and ends with E is 1/30.

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The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

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Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

Given that there are 200 yards between them and a 36 yard difference in height, the angle of elevation is 10.204°.

The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical notions are built. Trigonometry is used to establish directions like the north, south, east, and west. It also tells you the direction to point the compass in order to travel straight forward. To locate a certain location, it is used in navigation. It is also employed to calculate the separation between a location in the water and the coast.

Here,

p=36 yards

b=200 yards

tan θ=36/200

tan θ=0.18

θ=tan⁻¹(0.18)

θ=10.204°

The angle of elevation is 10.204° as distance between them is 200 yards and height is 36 yards.

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Answer:

28:20

Step-by-step explanation:

you just multiply 5 by 4 because 20 divided by 4 is 5 and then multiply 7 by 4

Answer:

Let total students be ‘X’

No of girls = (X-20)

Girls/Boys=7/5=(X-20)/20

7(20) =5(X-20)

140=5X-100

5X=240

X = 240/5

X =48

So, Total Students are 48

No of girls = (X-20) = 48-20 = 28

Step-by-step explanation:

Answer:

#4

Step-by-step explanation:

1) The y intercept is 0.

2) Convert to slope-intercept form:

2x + 3y = 12

3y = -2x + 12

y = -2/3 x + 4

So the y-intercept is 4.

3) Write in point-slope form:

y + 4 = 2 (x - 1)

Now convert to slope-intercept form:

y + 4 = 2x - 2

y = 2x - 6

So the y-intercept is -6.

4) The y-intercept is 5.

So of the four lines, #4 has the largest y-intercept.

The line with an  x-intercept of -1 and a  y-intercept of 1 is C. x - y = -1

A linear equation is of the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept

Given the line x - y = -1, the x intercept is at y = 0, hence:

x - 0 = -1

x = -1

The y intercept is at x = 0, hence:

0 - y = -1

y = 1

The line with an  x-intercept of -1 and a  y-intercept of 1 is C. x - y = -1

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Answer:

165°

..

..

..

..

..

..

.............

It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected

Let the number of fish collected in sample be represented as N.

Let the number of fish affected in it be represented by X.

Therefore, the proportion will be;

= X/N

Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.

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Answer:

P(x < 149.6) = 0.11821

Step-by-step explanation:

We start by calculating the z-score of the parameter given

Mathematically,

z-score = (x-mean)/SD/√n

z-score = (149.6-152.8)/26.2/√94

z-score = -3.2/2.70

z-score = -1.18

So the probability we want to calculate is;

P( x < -1.18)

we can use the standard normal distribution table to get this

From the standard normal distribution table, this value is 0.11821

The equation sin^2(x) = 1/2 - 1/2cos(2x) is an identity that holds true for all values of x. It can be used to simplify expressions involving sine and cosine functions.

The equation sin^2(x) = 1/2 - 1/2cos(2x) is a trigonometric identity, which means it holds true for all values of x. To understand why this identity is true, we can use the double angle formula for cosine, which states that cos(2x) = cos^2(x) - sin^2(x). Rearranging this formula gives sin^2(x) = cos^2(x) - cos(2x).

Now, we can substitute the identity cos^2(x) + sin^2(x) = 1 into the above equation, which gives sin^2(x) = 1 - cos^2(x) - cos(2x). Rearranging further gives sin^2(x) = 1/2 - 1/2cos(2x), which is the desired identity.

This identity can be useful in simplifying expressions involving sine and cosine functions. For example, if we have an expression with both sin(x) and cos(x), we can use this identity to express everything in terms of sin(x) or cos(x) only.

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Answer:

Domain: [-3, 3]

Range: [-1, 5]

Step-by-step explanation:

Reminder: domain is the x values that will make the function defined, and range is the possible y values the function could get.

Keeping that in mind, you can see that the domain of this function is [-3, 3] (using interval notation) and the range is [-1, 5].

Or, you could express the domain as -3≤x≤3 and the range as -1≤y≤5.

I hope this helped.

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

18

Step-by-step explanation:

The key of this leaf stem-leaf plot is:

4 | 5 = 45

Therefore, the data points that represents children with weight that is less than 50 pounds would be as follows:

First row => 12, 13, 15, 15 15, 16, 16, 19

Second row => 23, 25

Third row => 33, 35, 37, 38, 39

Fourth row => 44, 45, 45

Therefore, the number of children that weigh less than 50 pounds = 18

Answer:

C. Find the sum/difference.

1. 6 1/28

2. 7 2/9

3. 12 5/9

4. 9 14/15

5. 8 17/20

D. Add/Subtract

1. 9 2/15

2. 8 7/20

3. 8 9/10

4. 9 1/2

5. 7 5/9

E. Activity 3

1. 15 5/12 C.

2. 5 1/6 A.

3. 1 1/2 B.

4. 11 1/2 D.

5. N = 9 1/14 C.

F. Part 4

1. 16 7/40 C.

2. 16 7/15 A.