Let f, g and h be the functions from the set of integers to the set of integers defined by f(x) = 2x +3, g(x) = 3x + 2 and h(x) = x3 +1.

(a) Find (fºg)(x) (b) Find (gof)(x) (c) l'ind (f)(x) (d) Find (h+h)(x) (e) Find h-1(x)

The weight in pounds do the 30 small water bottles when the weight of one bottle is 5/8 pound is 75/4 pounds.

Weight measurement is the measurement of the heaviness of a object. The units of weight measurement are pounds, grams, kilograms etc.

A small size bottle of water which has the weighs 5/8 pound. One carton has total 30  small bottles of water.

Let the weight in pounds do the 30 small water bottles has is x. Thus,

\(x=\dfrac{5}{8}\times30\\x=\dfrac{5}{4}\times15\\x=\dfrac{75}{4}\rm\; pounds\)

Thus, the weight in pounds do the 30 small water bottles when the weight of one bottle is 5/8 pound is 75/4 pounds.

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The equation to solve the height of the trapezoid is 45h = 1,575

Given data ,

Let the area of the trapezoid be A

Now , the value of A = 1,575 cm²

And , the Top(base2) = 63cm and  Bottom(base1) = 27 cm

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

On simplifying , we get

1,575 = (63 + 27) / 2 x h

1575 = 45h

Hence , the equation is 1575 = 45h

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The complete question is attached below :

The trapezoid has an area of 1,575 cm2, Which equation could you solve to find the height of the trapezoid?

A 850.5h = 1,575

B 1,701h = 1,575

C 90h = 1,575

D 45h = 1,575

Top(base2) = 63 cm

Bottom(base1) = 27 cm

The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The correct answer is (a). The conclusion that the frequency of mothers' smoking is not related in any way to the incidence of influenza in their babies is a common correlation error.

The correct answer is (a) Conclusion: The frequency of mothers' smoking is not related in any way to the incidence of influenza in their babies. This conclusion makes a common correlation error by assuming that there is no relationship between smoking during pregnancy and the incidence of influenza in babies, just because there is a very low linear correlation coefficient.

It is important to note that correlation does not imply causation, and a low correlation coefficient does not necessarily mean that there is no relationship between the two variables. Therefore, this conclusion is invalid and incorrect.

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Answer:

\( \angle A \cong \angle D \)

Step-by-step explanation:

The Side-Angle-Side method cana only be used when information given shows that an included angle which is between two sides of a ∆, as well as the two sides of the ∆ are congruent to the included side and two sides of the other ∆.

Thus, since John already knows that \( \overline{AB} \cong \overline{DE} \) and \( \overline{AC} \cong \overline{DF} \), therefore, an additional information showing that the angle between \( \overline{AB} \) and \( \overline{DE} \) in ∆ABC is congruent to the angle between \( \overline{AC} \) and \( \overline{DF} \) in ∆DEF.

For John to prove that ∆ABC is congruent to ∆DEF using the Side-Angle-Side method, the additional information needed would be \( \angle A \cong \angle D \).

See attachment for the diagram that has been drawn with the necessary information needed for John to prove that ∆ABC is congruent to ∆DEF.

The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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Answer: Here's my real world scenario example:

A cookie shop decided to give away cookies to its customers. Normally, when the shop gives away zero cookies for free, they get 4 customers in a day. When they gave away one cookie for free, they got 8 customers in a day. When they gave away two cookies, they got 16 customers in a day. And when they gave away three cookies, they got 32 customers in a day.

I hope this helps! Feel free to give me Brainliest if you feel this helped. Have a good day, and good luck on your assignment. :)

Answer:

Option b

Step-by-step explanation:

To represent this proportion using fractions, let the numerators be the number of waffles sold and denominator, the number of sugar cones.

Thus, the proportion that can be used to represent the cone sales is

14/6 = 7/3

Answer:

BBBBBB

Step-by-step explanation:

we have the following:

solving for x:

therefore, the answer is the sales are $5350

The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%

We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:

standard error of the mean = standard deviation / √(sample size)

In this case, the standard error of the mean is:

standard error of the mean = 10 / √(6) = 4.08

To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.

The z-score is given by:

z-score = (sample mean - population mean) / standard error of the mean

In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:

z-score = (51 - 42) / 4.08 = 2.21

Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.

This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.

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Complete Question:

A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.

What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?

The value of exponential of -2 is 0.718

the exponential value of a number is equivalent to the number being multiplied by itself a particular set of times. The number to be multiplied by itself is called the base and the number of times it is to be multiplied is the exponent.

Exponential is also a mathematical term, meaning "involving an exponent." When you raise a number to the tenth power, for example, that's an exponential increase in that number.

The value of e^-2 is 0.718( 3 decimal place)

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In the given problem, we are asked to analyze three differential equations and identify regular singular points, find the exponents at each singularity, determine the indicial equation and its roots, find solutions, and discuss their properties. The first paragraph will focus on the Chebyshev equation and the Laguerre 13 differential equation, while the second paragraph will discuss the Bessel equation of order zero and its solution.

(a) For the Chebyshev equation, we observe that (1-x^2)y'' - xy' + α^2y = 0. Evaluating the coefficients, we find that both x = 1 and x = -1 are regular singular points. At x = 1, the exponents can be determined by substituting y = (x-1)^r into the differential equation and solving for r. Similarly, at x = -1, we substitute y = (x+1)^r. Solving for r in both cases will yield the exponents.

(b) Moving on to the Laguerre 13 differential equation, we note that xy'' + (1-x)y' + λy = 0. We can establish that x = 0 is a regular singular point by examining the coefficient of y'' in the equation. To find the indicial equation, we substitute y = x^r into the differential equation and solve for r. The roots of the indicial equation will provide information about the behavior of solutions near x = 0. Using these roots, we can construct the recurrence relation to generate solutions.

(c) Finally, considering the Bessel equation of order zero, x^2y'' + xy' + x^2y = 0, we can determine that x = 0 is a regular singular point by examining the coefficients of y'' and y' in the equation. The indicial equation is obtained by substituting y = x^r into the differential equation and solving for r, resulting in r(r-1) = 0. The roots are r1 = r2 = 0. One solution for x > 0 is the Bessel function of the first kind, J0(x), which can be expressed as an infinite series. It converges for all values of x.

These differential equations and their solutions have important applications in various areas of mathematics and physics, and understanding their properties and behaviors is crucial for solving problems in these fields.

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Answer:

D

Step-by-step explanation:

Since 2.7 is closer to 3 and shown in the graph.

The monthly instalment is 168.75 cedis (approx).

A trader borrowed an amount of 1800 Ghana cedis at an interest rate of 121/2 per cent per annum. It was agreed that the loan and the interest must be in one year equal instalments. The trader wants to calculate:
i) The interest on the loan
ii) The amount to be paid at the end of the year
iii) Monthly instalment.

i) Interest on the loan

The interest on the loan can be calculated using the formula:

I = PRT

Where,
P = Principal amount
R = Rate of interest per annum
T = time in years

Here,
P = 1800 cedis
R = 12.5% = 12.5/100 = 0.125
T = 1 year

I = 1800 × 0.125 × 1
I = 225 cedis

Therefore, the interest on the loan is 225 cedis.

ii) Amount to be paid at the end of the year

The amount to be paid at the end of the year can be calculated as:

Total amount = Principal + Interest

Total amount = 1800 + 225
Total amount = 2025 cedis

Therefore, the amount to be paid at the end of the year is 2025 cedis.

iii) Monthly instalment

If the loan and the interest are to be paid in one year equal instalments, then the monthly instalment can be calculated as:

Monthly instalment = Total amount / Number of months

Here,
Total amount = 2025 cedis
Number of months = 12
Monthly instalment = 2025 / 12
Monthly instalment = 168.75 cedis (approx)

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The required value of x for this polygon is - 90.

We know that,

Polygons are two-dimensional geometric figures with a fixed number of sides. A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges.

The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result.

A triangle with three sides is an example of a polygon. A circle is a plane figure, however it is not regarded a polygon because it is curved and lacks sides and angles.

As a result, we can argue that all polygons are 2d shapes, but not all two-dimensional figures are polygons.

Since,

Sum of interior angles of polygons = 360 degree

Therefore,

130 + x + 20 + 120 + 140 + x - 20 + 150 + x = 360

                                                                2x = 360 - 540

                                                                   x = -180/2

                                                                   x = -90

Thus,

The value of x = - 90

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To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted.

What is an Average?

In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.

It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.

When we analyze the  given question, we find that,

The total number of students were 49,

The true average was found to be 59k,

and the Sample average is found to be 44k.

Thus, in  the present question we will use the One- sample T-test.

We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.

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To convert an area from inches to centimeters, conversion factor should be 15.24 square centimeters.

To convert an area from inches to centimeters, we use the conversion factor of 2.54 cm per inch.

This means that for every inch, there are 2.54 centimeters. In order to find the area in centimeters, we first need to find the area in inches, and then multiply it by 2.54.

To find the area, we use the formula
=> area = length x width.

Let's say the length of a rectangle is 2 inches and the width is 3 inches. The area of this rectangle would be 6 square inches

=> (2 x 3 = 6).

To convert this area to square centimeters, we multiply the area in inches by 2.54.

So,

=> 6 square inches x 2.54 = 15.24 square centimeters.

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Answer:

this is the  answer \(x\geq 40\)

hope this helps!

Answer:

x is greater than or equal to 40

Step-by-step explanation:

30-90

-3/2x <-60

x>40

Answer:

-3.

Step-by-step explanation:

The first term  is -3x^4

and irs coefficient is -3.

the coefficiont of x2 must be 1, so divide the equation by 3

take half the coefficient of x and squared

then, add to both sides

Now we can rewrite the left side of the equation as a square term.

The price for 5 pounds of honey is $13.32.

Unitary method is a mathematical technique used to solve problems related to proportions and ratios.

To find the price for 5 pounds of honey, we can use a proportion:

Price of 3 pounds of honey / 3 = Price of 1 pound of honey

We can use this equation to find the price of 1 pound of honey, and then multiply by 5 to find the price of 5 pounds of honey.

Price of 3 pounds of honey / 3 = 7.99 / 3

Price of 1 pound of honey = 2.6633 (rounded to 4 decimal places)

Price of 5 pounds of honey = 2.6633 x 5 = $13.32 (rounded to 2 decimal places)

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Answer:

A

Step-by-step explanation:

The range refers to the possible y-values.  You can assume that values on the right column are the y-values if it is not specifically expressed.  The right column is the output, or y, column.

Since you have a table, you have to state each number.  Put the numbers in numerical order.  This gives you an answer of

{46, 49, 52, 53, 58, 63, 64, 67}

The set of data that provides the clearest difference between the two samples is option (c): One sample has M = 20 with s2 = 10 and the other has M = 30 with s2 = 10. The reason is that the standard deviation is higher in both samples compared to the other options, and the means of the two samples are also relatively far apart, making the difference between the two samples clearer. I

n options (a) and (b), the means are not far enough apart to provide a clear difference, and in option (d), while the means are farther apart than in option (b), the standard deviation is the same, which makes the difference less clear.

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Answer:

4th option

Step-by-step explanation:

The graph has a closed circle at x = 1 meaning x can equal - 1

Thus it must be an inequality involving ≤ or ≥

Since the arrow points to the left then it must be ≤

Then

3x + 1 ≤ 4 ( subtract 1 from both sides )

3x ≤ 3 ( divide both sides by 3 )

x ≤ 1

To find the margin of error (E) for a confidence level of c = 0.90, sample size (n) of 10, and sample standard deviation (s) of 3.1,

we need to determine the critical value from the t-distribution and then calculate the margin of error using the formula:

E = critical value * (s / sqrt(n))

The critical value is based on the desired confidence level and the degrees of freedom (d.f.) which depend on the sample size.

Since the sample size is 10, the degrees of freedom (d.f.) used in this case would be (n - 1) = (10 - 1) = 9.

To find the critical value corresponding to a 90% confidence level and 9 degrees of freedom, we can use a t-table or a statistical calculator. The critical value is approximately 1.83.

Now, we can calculate the margin of error (E):

E = 1.83 * (3.1 / sqrt(10))

E ≈ 1.83 * (3.1 / 3.162)

E ≈ 1.83 * 0.981

E ≈ 1.794

The value of the degrees of freedom (d.f.) used is 9.

Therefore, the correct answer is D) 1.80 with d.f. = 9.

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Answer:

Choice B) B \sqrt{29} 29 ​ square root of, 29, end square root = √29

Step-by-step explanation:

When given coordinates, the distance between those points(coordinates) is calculated as:

Distance = √(x2 - x1)² +(y2 - y1)²

Given(x1, y1), (x2, y2)

Fromm the question, we are given points(4,7) and (2,2)

Distance = √(x2 - x1)² +(y2 - y1)²

= √(2 - 4)² + (2 - 7)²

= √-2² + -5²

= √4 + 25

= √29

Therefore, Choice B is the answer = √29

The required greatest difference between the estimate and the true value is 45.

Given that,
Ethan needs to add together two whole numbers and wants to estimate the answer first. He rounds both numbers to 1 significant figure, which gives him 300 and 600 and adds them together to get an estimate of 900.

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,
For the estimated number 900, the least number that can be rounded to the number 900 is 855,
Now,
Difference  = 900 - 855 = 45

Thus, the required greatest difference between the estimate and the true value is 45.

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Hexadecimal and binary are two numbering systems that are commonly used in computing. Binary is a base-2 numbering system, which means it uses only two digits, 0 and 1, to represent all numbers. Hexadecimal, on the other hand, is a base-16 numbering system, which means it uses 16 digits, from 0 to 9 and A to F, to represent numbers.

One hexadecimal digit can represent 16 different values, while one binary digit can represent only two values (0 or 1). This means that one hexadecimal digit can represent 16 times as many values as one binary digit.

To understand this better, let's consider an example. The binary number 1111 is equivalent to the hexadecimal number F. In binary, 1111 can represent only one value, which is 15 in decimal. However, in hexadecimal, the digit F can represent 16 different values, from 0 to 15 in decimal.

Therefore, using hexadecimal notation can be more efficient and compact than using binary notation, especially when dealing with large numbers. In addition, hexadecimal is often used in computing to represent memory addresses, color codes, and other values that need to be represented in a compact and easily readable format.

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Answer:

  Pears:  30

Step-by-step explanation:

Constant:

  3x + 5x + 2x = 150

                 10x = 150

                    x = 15  

Multiply ratio with constant from above:

  oranges : apples

       3 * 15 : 5 * 15

            45 : 75       ==>               45 oranges: 75 apples

  pears : apples

   2 * 15 : 5 * 15

        30 : 75          ==>                    30 pears: 75 apples

Check:

45 oranges + 75 apples + 30 pears = 150 fruits