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The linear function that models the baby's weight, w, as a function of the age of the baby, in months, t, is equals to the w(t) = 11 + (1/2)t.

The a straight line graph represents linear function. The linear function form is, y = f(x) = a + bx. It has an independent variable and a dependent variable. There is independent and dependent variables are x and y respectively. We have provide a scenario which consists the following informations,

The weight of new born baby = 11 pounds

The weight gained by new born baby in one month = 1/2 pounds

We have to determine a linear function which models the baby's weight (w pounds), as a function of the baby's age, in months (t). From the definition of linear function, we see here weight of baby is an dependent variable and month in first year is independent. So, the linear function of weight of baby is written as w(t) = 11 + (1/2)t , where t represents months in baby's first year. Hence, required function is w(t) = 11 + (1/2)t.

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We can conclude after answering the provided question that Therefore, function g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.

In mathematics, a function appears to be a connection between two sets of numbers in which each member of one set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from a set and produces output from another. The variable x has now been frequently sometimes used represent the inputs, and the flexible y is used to represent the outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 represents a linear model in which each x-value yields a unique value of y.

So, g(x) = f(x + 3) = (x + 3)² = x² + 6x + 9.

g(x) = x² + 6x + 9

= 1(x² + 6x + 9)

= 1(x² + 6x + 9 + 9 - 9)

= 1((x + 3)² + 9 - 9)

= 1(x + 3)² + 0

Therefore, g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.

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Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

cos(3x - 180°) = cos(180° - 3x)

cos(180° - 3x) = -√3/2

-cos(3x) = -√3/2

cos(3x) = √3/2

3x = π/6

x = π/18

Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.

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A. To construct a grouped frequency distribution for the given data, we first need to determine the range of the data:

Range = Maximum value - Minimum value

Range = 39 - 5

Range = 34

Next, we need to decide on the width of each class interval. A common rule is to choose the number of classes to be between 5 and 20, and then choose a class width that is a convenient number. In this case, we will choose 8 classes and a class width of 5.

Class width = Range / Number of classes

Class width = 34 / 8

Class width ≈ 4.25

We can round up the class width to 5 to get a convenient number. The class intervals are:

5 - 9.99

10 - 14.99

15 - 19.99

20 - 24.99

25 - 29.99

30 - 34.99

35 - 39.99

40 - 44.99

Next, we count the number of observations that fall into each class interval. This gives us the frequency of each interval. The grouped frequency distribution is:

Class Interval Frequency

5 - 9.99 5

10 - 14.99 8

15 - 19.99 9

20 - 24.99 16

25 - 29.99 7

30 - 34.99 6

35 - 39.99 1

40 - 44.99 0

B. To draw the histogram, frequency polygon, and cumulative frequency curves, we first need to calculate the cumulative frequencies. The less than cumulative frequency is the running total of the frequencies up to each class interval, while the more than cumulative frequency is the running total of the frequencies from each class interval to the end.

Class Interval Frequency Less than Cumulative Frequency More than Cumulative Frequency

5 - 9.99 5 5 62

10 - 14.99 8 13 57

15 - 19.99 9 22 49

20 - 24.99 16 38 40

25 - 29.99 7 45 24

30 - 34.99 6 51 17

35 - 39.99 1 52 11

40 - 44.99 0 52 10

Now we can draw the graphs:

Histogram:

   20 |

       |           __

       |          |  |

       |    __    |  |

       |   |  |   |  |

       |   |  |   |  |

       |   |  |   |  |

       |___|__|___|__|__

           5  10  15  20

Frequency polygon:

   25 |

       |  __

       | |  |     __

       | |  |    |  |

       | |  |    |  |

       | |  |

Answer:

you didn't say which process to use while solving so I have used graphical method but I hove it's useful

The appropriate scenario to conduct a paired t-test for means is when we have two related samples, and we want to test whether there is a significant difference in the means between the two samples. Hence, B, D, and E are the appropriate responses.

A t-test is a statistical test used to determine whether two sets of data are significantly different from each other, based on their means. It is a parametric test, meaning it makes certain assumptions about the data, such as that it is normally distributed and that the variances of the two groups being compared are equal.

There are several types of t-tests, including the independent samples t-test, which is used when comparing two groups that are not related to each other, and the paired samples t-test, which is used when comparing two groups that are related or paired, such as before-and-after measurements from the same individuals.

B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.

D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.

E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.

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The volume of the cylinders are;

1.  602. 88 cm³

2.  56.52 cm³

3.  141. 3 cm³

The formula for calculating the volume of an open cylinder is expressed as;

V = πr²h

Such that the parameters are;

Then, we have;

Substitute the values

1. Volume = 3.14 × 4² × 12

Multiply the values after finding the square

Volume = 602. 88 cm³

2. Substitute the values

Inner radius, r = 2cm

Volume =3.14 × 1.5 ² × 8

Multiply the values, we get;

Volume = 56.52 cm³

3. Substitute the values

Inner radius = 2cm

Volume = 3.14 × 3² × 5

Multiply the values

Volume = 141. 3 cm³

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The area of remaining sheet is 536 cm²

Since, we know that the area of circle [tex]=\pi \times r^2[/tex]

Area of bigger circle [tex]=\dfrac{22}{7} \times14\times14[/tex]

[tex]=44\times14[/tex]

[tex]=616 \ \text{cm}^2[/tex]

Thus, the area of bigger circle is 616 cm²

Similar way, the area of 2 smaller circles [tex]=2\pi r^2[/tex]

[tex]=2\times\dfrac{22}{7} \times3.5\times3.5[/tex]

[tex]=44\times0.5\times0.5[/tex]

[tex]=77 \ \text{cm}^2[/tex]

Thus, the area of 2 smaller circle is 77 cm²

[tex]\text{Area of rectangle}=\text{Length}\times\text{Breadth}[/tex]

[tex]=3\times1=3 \ \text{cm}^2[/tex]

Thus, the area of rectangle is 3 cm²

Now, remaining area of sheet = Area of bigger circle − Area of both smaller circle − Area of rectangle

[tex]=616-77-3=536 \ \text{cm}^2[/tex]

Hence, area of remaining sheet is 536 cm²

The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.

An expression is a mathematical phrase that can contain numbers, variables, operators, and sometimes functions. Expressions are used to represent or calculate values, and they can be simple or complex. For example, "2 + 3" is a simple expression that can be evaluated to give the value 5, while "3x + 2y - 4" is a more complex expression that contains variables and can only be evaluated if values are assigned to the variables. Expressions can also be combined to form more complex expressions using operators like addition, subtraction, multiplication, and division.

To find the inverse function of g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)), we can follow these steps:

Step 1: Replace g(x) with y, so that the function becomes g'(x) = -y.

Step 2: Solve the equation for y in terms of x: y = - g'(x) = - (sqrt(x) + 6)/(1 - sqrt(x)).

Step 3: Interchange x and y: x = - (sqrt(y) + 6)/(1 - sqrt(y)).

Step 4: Solve for y in terms of x:

[tex]x = - (sqrt(y) + 6)/(1 - sqrt(y))\\x(1 - sqrt(y)) = -sqrt(y) - 6\\x - x sqrt(y) = -sqrt(y) - 6\\x + 6 = (x + 1) sqrt(y)\\(x + 6)/(x + 1) = sqrt(y)\\[/tex]

[tex]y = [ (x + 6)/(x + 1) ]^2[/tex]

Therefore, the inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is:g^-1(x) = [ (x + 6)/(x + 1) ]^2[/tex]

Note that this function is defined for all x except x = 1, where the original function g(x) is not defined. Therefore, g(x) is not invertible at x = 1.

Therefore, The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.

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Answer:

Step-by-step explanation: ¼ +6 ⅓;

= [tex]\frac{1}{4}[/tex] +[tex]\frac{19}{3}[/tex];

= [tex]\frac{3+76}{12}[/tex];

= [tex]\frac{79}{12}[/tex];

= 6[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

Well to add fractions, you should make the denominator (denominator means the lower part for example 4 in ¼) the same for all numbers.

Forget the 6 for now, take only ¼ and ⅓ into consideration, make it have the same denominator

For 1/4 you multiply both up and down by 3 so it will become 3/12

For 1/3, multiply both by 4, so it becomes 4/12

You now have 3/12 and 4/12, let's not forget about the 6 now.

How do you obtain 6 if you have to make 12 denominator? (If you do 12×6 you get 72 right?) so 6 = 72/12

Your answer will be obtained like this

1/4 + 6 + 1/3 = 3/12 + 72/12 + 4/12 = 79/12 and you can make it a whole number if you can.

Ans : 79/12 which is also equal to 6 and 7 over 12 (6 7/12)

The correct answer is: They are both 1 standard deviation away from their means, but in opposite directions. The first score is 1 standard deviation below mean, while second score is 1 standard deviation above the mean.

Standard deviation is a measure of the deviation or spread from the mean (mean) of a set of data values. 

More specifically, the standard deviation is calculated by taking the square root of the variance of the data. Variance is the mean square of the difference of each data point from the mean. 

The first score of 40 from a distribution with a mean of 50 and a standard deviation of 10 is 1 standard deviation below the mean, because it is (50-40)/10 = -1 standard deviation from the mean.

The second score of 45 from a distribution with a mean of 50 and a standard deviation of 5 is 1 standard deviation above the mean, because it is (45-50)/5 = -1 standard deviation from the mean.

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You can expect the coin to land on heads 2 times when it is tossed 4 times, on average.

7. True, 8. True, 9 No, because every name had an equal chance of being drawn from the jar, 10. False

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.

7. True: Sampling bias: unequal chance of selection leading to unrepresentative samples.

8. True: Avoiding bias: random sampling, representative samples, and minimizing nonresponse bias.

9 No, because every name had an equal chance of being drawn from the jar.

10. False: Biased sample: unrepresentative sample due to factors like nonresponse or small sample size.

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Answer:

1302

Step-by-step explanation:

The quotient using a synthetic method of division is 3x² - x + 10 - 64/(x + 7)

The quotient expression is given as

(3x³ + 20x² + 3x + 6) divided by x + 7

Using a synthetic method of quotient, we have the following set up

-7 |   3    20   3   6

    |__________

Bring down the first coefficient, which is 3:

-7 |   3    20   3   6

    |__________

       3

Multiply 3 by -7 to get -21, and write it below the next coefficient and repeat the process

-7 |   3    20   3   6

    |____-21__7_-70____

       3      -1   10    -64

So, the quotient is 3x² - x + 10 and the remainder is -64

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Answer:

For #17:

This is a 45-45-90 triangle. Therefore, the missing side length (x) is equal to the other leg of the triangle, which is 6.

For #18:

This is a 30-60-90 triangle. Therefore, the missing side length (m) is equal to the hypotenuse (18) divided by 2, or 9.

For #19:

This is a 30-60-90 triangle. Therefore, the missing side length (y) is equal to the hypotenuse (12) multiplied by the square root of 3, or 12√3.

For #20:

This is a 30-60-90 triangle. Therefore, the missing side length (u) is equal to the short leg (5√3) multiplied by 2, or 10√3.

For #21:

This is not a right triangle because the angles do not add up to 180 degrees.

For #22:

This is a right triangle because the angles add up to 180 degrees and one of the angles is 90 degrees.

Step-by-step explanation:

the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

To determine if the function f: P(A) → P(A), where f(X) = A-X, is onto, one-to-one, neither, or both, we need to consider the following:

Onto: A function is onto if every element in the codomain has a corresponding preimage in the domain. In other words, for every Y in P(A), there exists an X in P(A) such that f(X) = Y.

Let Y be any subset of A. Then, we need to find an X such that f(X) = Y. Since f(X) = A-X, we need to find an X such that A-X = Y. Solving for X, we get X = A-Y. Therefore, we can choose X = A-Y, and we have f(X) = A-(A-Y) = Y. Hence, f is onto.

Next, we need to prove that f is not one-to-one. To do this, we need to find two different sets X1 and X2 such that f(X1) = f(X2).

Hence, the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.

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Answer:

3. 5.3 ft

4. 4.5 ft

Step-by-step explanation:

3.

Let's call the height of the connection point on the tree "h". We can use trigonometry to relate the angle and the length of the guy wire to "h". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the height "h", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:

sin(42) = h / 8

To solve for "h", we can multiply both sides by 8:

h = 8 sin(42)

Using a calculator, we get:

h ≈ 5.3 feet

So the height of the connection point on the tree is about 5.3 feet, to the nearest tenth of a foot.

4.

The ladder, the wall, and the ground form a right triangle, with the ladder being the hypotenuse. Let's call the height on the wall that the ladder reaches "x". We can use trigonometry to relate the angle and the length of the ladder to "x". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the height "x", and the hypotenuse is the length of the ladder, which is 5 meters. So we have:

sin(65) = x / 5

To solve for "x", we can multiply both sides by 5:

x = 5 sin(65)

Using a calculator, we get:

x ≈ 4.5 meters

So the ladder reaches a height of about 4.5 meters on the wall.

The triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.

In mathematics, congruent means that two shapes or objects have the same size and shape. They match exactly when superimposed on each other. Congruence also applies to angles, where two angles are said to be congruent if they are equal in measure. Congruence can also refer to the equality of two expressions, where two expressions are congruent when they have the same value. In other words, congruence is a term used to describe a relationship between two objects or shapes that are exactly the same size and shape.

In order to prove that two triangles are similar, we need to show that their corresponding angles are congruent. Given that angles T, X, and U are all equal, and angles X, U, and Y are all equal, we can therefore conclude that angles T and Y are also equal. This means that triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.

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The corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write : TUV ~ XYZ

What is congruent?

Congruent is a term used in geometry to describe two figures or objects that have the same shape and size. In other words, if two figures are congruent, they are identical in every way, except that they may be oriented differently or located in different positions in space.

To prove that TUV ~ XYZ, we need to show that the two triangles are similar, which means that their corresponding angles are congruent and their corresponding sides are in proportion.

Given that T=​X=U=Y, we can conclude that angle TUV and angle XYZ are congruent, and angle TVU and angle YXZ are also congruent. These two angles are the corresponding angles that are congruent in the two triangles.

To show that the corresponding sides are in proportion, we need to compare the ratios of the corresponding side lengths. We can start by comparing the ratio of the lengths of TU and XY:

TU / XY = (TU / TX) * (TX / XY) (by the transitive property of equality)

TU / TX = 1 (because T = X)

TX / XY = 1 (because U = Y)

Therefore, TU / XY = 1 * 1 = 1.

Similarly, we can compare the ratio of UV and YZ:

UV / YZ = (UV / UY) * (UY / YZ) (by the transitive property of equality)

UV / UY = 1 (because U = Y)

UY / YZ = 1 (because T = X)

Therefore, UV / YZ = 1 * 1 = 1.

Therefore, the corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write:

TUV ~ XYZ

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Answer:

The smallest number of cars that can tailgate in a straight line at a football game is 12.

Step-by-step explanation:

Smallest Tailgate Cars Number

This can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.

This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.

Answer:

3

Step-by-step explanation:

basicly one car will be in the back one in the middle and one in the front. if I'm correct then it should be 3

The coordinate of the fourth vertex is determined as (13,-23).

To find the fourth vertex of the parallelogram, we need to use the fact that opposite sides of a parallelogram are parallel and equal in length.

Let's start by finding the vectors for two sides of the parallelogram. We can use the given coordinate points to find the vectors:

Vector AB = (xB - xA, yB - yA) = (-7 - (-5), -11 - (-3)) = (-2, -8)

Vector BC = (xC - xB, yC - yB) = (4 - (-7), -13 - (-11)) = (11, -2)

Since opposite sides of a parallelogram are parallel, we know that these two vectors are parallel.

To find the fourth vertex, we can add the vector AB to the endpoint of vector BC:

Vector CD = Vector BC + Vector AB = (11, -2) + (-2, -8) = (9, -10)

Now we can add this vector to point C to find the coordinates of point D:

Point D = (xC + CDx, yC + CDy) = (4 + 9, -13 - 10) = (13, -23)

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Answer:

OP = 424: CE = 79,5

Step-by-step explanation:

I added a photo of my solution

The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.

The system of equations to find the smallest number of busses the orchestra can rent is,

The total number of buses :

b + v ≤ 6

The total number of passengers.

25b + 12v ≥ 111 - - - - (2)

Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

The odds in favor of it raining tomorrow are 1 to 6.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

To find the odds in favor of it raining tomorrow, we need to calculate the ratio of the probability that it will rain to the probability that it won't rain. The probability that it won't rain is 1 - 1/7 = 6/7.

So, the odds in favor of it raining are:

Probability of raining / Probability of not raining

= (1/7) / (6/7)

= 1/6

Therefore, the odds in favor of it raining tomorrow are 1 to 6.

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The cumulative area corresponds to the​ z-score is 1.67

What is the cumulative area?

The likelihood that a real-valued random variable, X, will assume a value less than or equal to x is represented by the cumulative distribution function of X, or simply by the distribution function of X, assessed at x.

Here, we have

Given: the following cumulative area is 0.952.

We have to find the Z-score that corresponds to the following cumulative area.

p(z<z)=0.952

p(z<1.67)=0.952

z=1.67 (from the standard normal table)

Hence, The cumulative area corresponds to the​ z-score is 1.67

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Answer:

There is no y intercept because the graph does not cross the y axis.

The x intercept is (-2,0)

Step-by-step explanation:

Helping in the name of Jesus.