phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebe’s hunch?

Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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No, the given value of h=2 is not a solution of the equation 1/3h=6.

The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.

A type of motion known as upward motion involves an item moving up against the pull of gravity.

The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.

The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.

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Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.

In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:

">" which means "greater than"

"<" which means "less than"

"≥" which means "greater than or equal to"

"≤" which means "less than or equal to"

Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.

Here,

The formula for the circumference of a circle in terms of its diameter is:

C = πd

where π (pi) is approximately 3.14.

We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:

9.9 ≤ 3.14d ≤ 10.2

Dividing all sides of the inequality by 3.14, we obtain:

3.15 ≤ d ≤ 3.24

Rounding to three decimal places, the corresponding interval for the diameters of the washers is:

3.150 ≤ d ≤ 3.240

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For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].

The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].

given

The collection of all x-values for which h(x) is specified is the domain of the function h.

The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.

The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.

The range is therefore [-3, 0].

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The complete question is :-  The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.

-2

-3-

4-

domain =

range =

Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

Step-by-step explanation:

Perimeter

Pls mark me brainliest

The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a p-value of 1-∝.

So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]

Now, find M as such

[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ

In which is the standard deviation of the population and n is the size of the sample.

[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.

The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.

So the correct answer is:

(91331.94, 113352.06)

Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.

Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.

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Complete Question:

A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices

A). (89869.82, 114814.18)

B). (90292.73, 114391.27)

C). (91331.94, 113352.06)

D). (90371.37, 114312.63)

Answer:Given : number of hours spent studying for a history final exam and the score on that exam.

To Find : Which value is an outlier

(1.5, 65)

(3.5, 71)

(4.5, 98)

(6.5, 88)

Solution:

Number of hours spent studying =x            

Exam score   = y

x         y

1.5       65

2         68

3.5      71

4.5      98

6         82

1.5 -   2   difference = 0.5

2 - 3.5     difference = 1.5

3.5 - 4.5   difference = 1

4.5 - 6       difference = 1.5

No outlier

65  - 68   Difference  3

68 - 71      Difference  3

71 -  98      Difference  27

71 - 82     Difference  11

Hence 98 is outlier

(4.5    ,  98 )  is outlier

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Mrs. Juarez graded ten English papers and recorded the scores. 92 ...

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first quartile is 20 then semi-inter quartile range is

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Step-by-step explanation:

Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)

Answer:

A ,B ,C

Step-by-step explanation:

2+2+2+2 equals 8

4x2 equals 8 and

1x8 equals 8

Answer:

A) 2 + 2 + 2 + 2

B) 4 × 2

C) 1 × 8

Hope this helps!

Step-by-step explanation:

A = 4 + 4 = 8

B = 8

C = 8

D = 16

E = 16

Therefore , the solution of the given problem of mean comes out to be  15 is the solution.

The sum of all values divided by all of the values constitutes the result from a collection, also referred to as the arithmetic mean. It is often referred to be known as "mean" as well as is one of the most frequency used main trend indicators. To find the answer, multiply the collection's overall amount of numbers by all of its values. Either the original data or data which has been combined into frequency charts can be used for calculations.

Here,

We can use linear interpolation between the two closest latitude numbers in the table, 45 and 50, to determine the typical temperature for a city with a latitude of 48.

Let T(45) and T(50) represent the typical temperatures at respective latitudes of 45 and 50, respectively. The following algorithm can be used to determine the temperature at 48 degrees latitude:

=> T(48) = T(45) + (T(50) - T(45)) * (48 - 45)/(50 - 45)

Using the numbers from the table as inputs, we obtain:

=> T(48) = 14 + (16 - 14) * (48 - 45)/(50 - 45)

=> T(48) = 14 + 2 * 3/5

=> T(48) = 14 + 1.2

=> T(48) = 15.2

The estimated average temperature for a city with a latitude of 48 is 15, rounded to the closest whole number.

Consequently, 15 is the solution.

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From the given data of hunters and do we find out there are 9 hunters and 15 dogs.

Let's assume that there were "h" hunters and "d" dogs.

Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:

2h + 4d = 78

We can simplify this equation by dividing both sides by 2:

h + 2d = 39

We also know that there were 24 heads in total, which includes the hunters and the dogs:

h + d = 24

We can now solve these two equations simultaneously to find the values of h and d.

First, we can solve for h in terms of d from the second equation:

h = 24 - d

We can substitute this expression for h in the first equation:

(24 - d) + 2d = 39

Simplifying and solving for d:

d = 15

Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:

h + d = 24

h + 15 = 24

h = 9

Therefore, there were 9 hunters and 15 dogs.

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Step-by-step explanation:

1. Draw a line of 8cm.

2. Take a compass and keep it in the length of more than 8 cm.

3. Draw an arc from point A and B which will intersect at point between A and B.

4. Draw a straight line from the arc.

5. You will find out that the line will be drawn exactly between A and B at 4cm.

The required ratio of  is (a + c) : c 11:8.

Given that a:b=1:4 and b:c=3:2.

We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.

To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:

[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]

Therefore, the ratio [tex]$(a+c):c$[/tex] is:

[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]

Hence, the required ratio is 11:8$.

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Using coefficients ak, the following product may be extended into a power series: the expression is provided in the attached file. For each of the [tex]k 2 N[/tex]phrases, determine the coefficients ak before them. The formula [tex]ak = (-1)k(k+1)/2[/tex] yields the coefficients ak.

To get the coefficients ak, we may first simplify the above formula by factoring out a -x and rearranging terms. This results in the equation: [tex](1-x)/(1+x)2 = -x/(1+x) - x2/(1+x)2.[/tex]

Now, each term in the statement may be expanded into a power series using the formula for the geometric series. This results in: Both[tex]-x/(1+x) and -x2/(1+x)2[/tex] are equal to[tex]-x + x + x + 2 + x + 3 +...[/tex]

By combining like terms and adding these two power series, we can determine that the coefficient in front of [tex]xk is (-1)k(k+1)/2.[/tex]  Hence,[tex]ak = (-1)k(k+1)/2[/tex] is the formula for the coefficients ak.

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The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.  

a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .

Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.

Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.

So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.

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a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.

b) The mean salary of the given model by using the probability density function is approximately $270.86.

a) The cumulative distribution function of the given random variable is provided as follows:

F(x) = {1−kx^−3 if x>44000, and 0 otherwise

The cumulative distribution function is given as

F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)

We need to check the value of the cumulative distribution function at 44000

We have, F(44000) = 0

0 = 1−k(44000)^−3

⇒ 1 = k(44000)^−3

⇒ k = 1/(44000)^−3

⇒ 5.427 x 10^−12

Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)

Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68

b) The probability density function is given as,

f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise

The mean or expected value of the random variable is given as

E(X) = ∫[−∞,∞]xf(x)dx

= ∫[44000,∞]x(3kx^−4)dx

= 3k∫[44000,∞]x^−3dx

= 3k[(−1/2)x^−2] [∞,44000]

= (3k/2)(44000)^−2

= 270.86 (approx.)

Therefore, the mean salary given by the model is $270.86 (approx.)

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Answer:

D

Step-by-step explanation:

The square root of 50 is approximately equal to 7.07

-7.1111… can be rounded to -7.11

23/3 is equal to approximately 7.67

-7 1/5 is equal to -7.2

By using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429.

The Euler's method is used to estimate a numerical solution of a first-order differential equation. The formula of Euler's method is given by:

y_1 = y_0 + hf(x_0, y_0)

Where: y_1 is the next value of y after one iterationy

0 is the initial value of yy' = f(x, y)h is the step size

This method is an iterative procedure that advances the estimate of y by one step by approximating the curve using a tangent line at each point along the curve.

Given that y(0) = 4 and h = 0.2, we can use Euler's method to estimate y(1) where y(x) is the solution of the initial-value problemy' = x2 + xy, y(0) = 4

Using Euler's method with a step size of 0.2, we get:

1) When x = 0, y = 4

y_1 = y_0 + hf(x_0, y_0) = 4 + 0.2(0 + 4(0))= 4.02

When x = 0.2, y = 4.02

y_2 = y1 + hf(x_1, y_1) = 4.02 + 0.2(0.2^2 + 0.2(4.02))= 4.10523

When x = 0.4, y = 4.1052

y_3 = y_2 + hf(x_2, y_2) = 4.1052 + 0.2(0.4^2 + 0.4(4.1052))= 4.1994144

When x = 0.6, y = 4.1994

4 = y_3 + hf(x_3, y_3) = 4.1994 + 0.2(0.6^2 + 0.6(4.1994))= 4.3032545

When x = 0.8, y = 4.3033

y_5 = y_4 + hf(x_4, y_4) = 4.3033 + 0.2(0.8^2 + 0.8(4.3033))= 4.4174496

When x = 1, y = 4.4174

y_6 = y_5 + hf(x_5, y_5) = 4.4174 + 0.2(1^2 + 1(4.4174))= 4.5429404

Therefore, using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429 (rounded to four decimal places).

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The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.

The term "intersect" typically refers to the point or points where two or more things, such as lines, curves, sets, or geometrical shapes, meet or cross each other. The intersection can be described as the common elements or properties shared by the different objects or sets that intersect.

The graph of the equation Y=-2x+4 is a straight line with a slope of -2 and a y-intercept of 4. To graph this equation, you can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To graph Y=-2x+4, follow these steps:

The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.

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Answer:

9 words

Step-by-step explanation:

We know

He has 12 words to memorize, and he is 3/4 done.

How many words has Pablo memorized so far​?

We Take

12 x 3/4 = 9 words

So, Pable has memorized 9 words.

The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).

The probability of Z > 0.75 is 1 - 0.77337 = 0.22663

The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968

Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).

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the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)

Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt

Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C

a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt

Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.

Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,

we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:

S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)

dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change

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The approximate Z-score for this recruit is b. 0.18.

The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.

The approximate Z-score for this recruit. The formula for Z-score is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,

Z=(23-22.8)(1.1)

Z=0.2/1.1

Z [tex]\approx[/tex] 0.18

Thus, the approximate Z-score for this recruit is b. 0.18.

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Answer:

We know that A receives R500 less than C, so we can write:

4x = 9x - 500

Solving for x, we get:

5x = 500

x = 100

Now we can calculate the amounts received by each person:

A = 4x = 4(100) = R400

B = 7x = 7(100) = R700

C = 9x = 9(100) = R900

To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:

A:B = 400:700 = 4:7

B:C = 700:900 = 7:9

Therefore, the total amount divided is:

400 + 700 + 900 = R2000

So the amount that is divided is R2000.

Step-by-step explanation:

The total amount of money divided is R2000.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of A, B and C= 4:7:9

Now,

Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:

4x + 500 = C's share

We can also write an equation to represent the fact that the three shares add up to the total amount:

4x + 7x + 9x = T

Simplifying this equation, we get:

20x = T

Now we can substitute the first equation into the second equation and solve for x:

4x + 7x + (4x + 500) = 20x

15x + 500 = 20x

500 = 5x

x = 100

Now we can find the individual shares by multiplying x by the appropriate ratio factor:

A's share = 4x = 400

B's share = 7x = 700

C's share = 9x = 900

Finally, we can check that these add up to the total amount:

400 + 700 + 900 = 2000

Therefore, by the given ratio the answer will be R2000.

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