On his first biology test, Bob received the following scores: 72, 86, 92, 63, and 77. What test score must Bob earn on his sixth test so that his average (mean score) for all six tests will be 80?

This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.

A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.

Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.

by the question.

let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:

\(f(x) = (1.20x) + 2\)

In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.

We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:

\(g(x) = 1.20x\)

\(h(x) = x + 2\)

Using function composition, we can write the function for the worker's new hourly wage as:

\(f(x) = h(g(x)) = h(1.20x) = 1.20x + 2\)

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Answer:

slope=1/4

y-intercept=3

y=.25x+3

Step-by-step explanation:

slope=rise over run so

slope=1/4

y-intercept is the value of y where the line crosses the y axis..

y-intercept=3

In y=mx+b form m is slope and b is y-intercept so...

y=.25x+3

Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4\(\neq\)9, 1\(\neq\)9, 8\(\neq\)9, and 7\(\neq\)9 then 9 is not an element of this set and the statement is true.

Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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According to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

Since p:q:r = √3:1:1, we can write:

p = √3x

q = x

r = x

where x is a common factor.

We can see that triangle ABC is a 30-60-90 triangle with angle A = 60 degrees, and that angle BOC is a right angle. Therefore, we can use the ratios of sides in a 30-60-90 triangle to find the values of P, O, and R:

P = AB = p = √3x

O = BC/2 = q/2 = x/2

R = AC = r = x

Therefore, the ratio P:O:R is:

P:O:R = √3x : x/2 : x

We can simplify this ratio by multiplying all terms by 2 to get rid of the fraction:

2√3x : x : 2x

We can further simplify by dividing all terms by x:

2√3 : 1 : 2

Therefore, according to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

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If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

An equation is an expression that shows the relationship between two or more variables and numbers.

There are 6 days from Monday to Saturday. The factory is closed on Tuesday and 15000 packets were packed on Monday. If no less than 100000 packet must be packed, hence:

4x + 15000 ≥ 100000

x ≥ 21250

If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

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A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point X (0, 4)  →  Coordinates of point Y = (0, -4)

Coordinates of point X (1, 3)  →  Coordinates of point Y = (-1, -3)

In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.

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Answer:

1 4/5

Step-by-step explanation:

198 woman to 110 is basically a ratio, so we should put it like this: 198:110

Now, a ratio that needs to be simplified is basically a fraction, so: 198/110

Now we divide the fraction.

First, find the GCF of both numbers.

The GCF of 198 and 110 are both 22.

Now we divide, and we get 9/5, and we turn it into a mixed number, 1 4/5.

The value of the double integration is 7776 after solving and integration. the answer is 7776.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

Double integration (x + y) dA

y = x²

y² = 216x

y = √216 √x

∫∫(√216 √x +  x²)

After solving:

\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)

=7776

Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.

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Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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Answer:

EIGHT divided by EIGHT

Step-by-step explanation:

The 8/8 word form is EIGHT divided by EIGHT

Answer:

eight over eight

Step-by-step explanation:

there can be multiple verbal forms of this such as

eight over eight

one

complte eght over the whole eight

or just plain ol' one because eight over eight equals one

Answer:

what is the expressio

Step-by-step explanation:

The surface area of the cone is 163.3 in². The result is obtained by using the formula for surface area of a cone.

A cone has a base area and the curved surface. The surface area of a cone can be expressed as

A = πr² + πrs

Where

We can get slant height by

s = √(h² + r²)

Where h is height of cone.

We have a cone with

Find the surface area!

A = πr² + πrs

A = 3.14(4)² + 3.14(4)(9)

A = 50.24 + 113.04

A = 163.28

A ≈ 163.3 in²

Hence, the cone has a surface area of 163.3 in².

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Answer:

2

Step-by-step explanation:

Given: 5 quiz scores of a student in a statistics course are 6,6, 5, 8, 10

To find:  standard deviation of the population

Solution:

Mean (M) = \(\frac{\sum_{i=1}^{n}x_i}{n}\)

here, \(x_i\) denotes number of observations and n denotes number of observations.

Variance = \(\frac{\sum_{i=1}^{n}(x_i-M)^2}{n-1}\)

Standard deviation = \(\sqrt{variance}\)

\(M=\frac{6+6+5+8+10}{5}=\frac{35}{5}=7\)

Variance = \(\frac{\sum_{i=1}^{n}(x_i-7)^2}{n-1}\)

\(=\frac{\left [ (6-7)^2+(6-7)^2+(5-7)^2+(8-7)^2+(10-7)^2 \right ]}{5-1}\\=\frac{1+1+4+1+9}{4}\\=\frac{16}{4}\\=4\)

Standard deviation = \(\sqrt{4}=2\)

Answer:

0.3333 = 33.33% of this group likes chocolate

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

Of the friends who like sprinkles, what proportion of this group likes chocolate:

So,

Event A: Likes sprinkles

Event B: Likes chocolate

15% of your friends like sprinkles (S) topping.

This means that \(P(A) = 0.15\)

5% of your friends like Chocolate (C) and also like sprinkles (S).

This means that \(P(A \cap B) = 0.05\)

So

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.05}{0.15} = 0.3333\)

0.3333 = 33.33% of this group likes chocolate

The value of angle B is 68 degrees and the length of the segments b is 27.81 and c is 11.28.

A triangle's sides and angles are related by the Law of Sines, a trigonometric formula. It specifically specifies that for all three sides and angles of the triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. This may be expressed as the following equation:

sin A/a = sin B/b = sin C/c

where a, b, and c are the lengths of the sides that are on each side of the triangle's three angles, A, B, and C.

For the give triangle we can use the Law of sines to find the missing values.

The law of sine is given as:

sin A/a = sin B/b = sin C/c

Given A = 90 degrees and C = 22 degrees,

sin 90 / 30 = sin 22 / c

c = 30 sin 22 / sin 90

c = 30 (0.37) / 1

c = 11.28

Now, Using the sum of triangles:

90 + 22 + B = 180

112 + b = 180

B = 68

Now,

sin A/a = sin B/b

Sin 90 / 30 = sin (68) / b

b = 30 sin (68)  sin 90

b = 27.81

Hence, the value of angle B is 68 degrees and the length of the segments b is 27.81 and c is 11.28.

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Answer:

E. Table.

Step-by-step explanation:

Since the data is numerical and discrete, a table would be the best way to present this data to an audience. A table can clearly and efficiently display all of the values in an organized manner. Additionally, a table could easily be used to calculate measures of central tendency, such as the mean or median.

Answer:

9x - 2x + 62 = 9x + 24

Number of correct answer each obtained = 19

Step-by-step explanation:

Given that:

Number of correct answers = x

POINTS for correct answers = 9

POINTS for incorrect answers = - 2

SCHOOL A:

Number of correct answers = x

Number of incorrect answers = x

Initial point = 62

Initial point + 9(number of correct answers) + - 2(number of incorrect answers)

62 + 9x - 2x

SCHOOL B :

Number of correct answers = x

Number of incorrect answers = 0

Initial point = 24

Initial point + 9(number of correct answers) + - 2(number of incorrect answers

24 + 9x

Since they end up tied :

School A = School B

62 + 9x - 2x = 24 + 9x

9x - 2x + 62 = 9x + 24

Number of correct answers gotten :

9x - 2x + 62 = 9x + 24

7x + 62 = 9x + 24

7x - 9x = 24 - 62

-2x = - 38

x = 19

Hence, Number of correct answers each obtained = 19

In response to the question, we may say that As a result, the bookstore expression had 800 books before the holiday.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

Let's name the number of books in the shop before to the holiday "x."

We know that the shop sold 25% of its books over the holiday, hence 75% of the books remained after the holiday.

This information may be expressed as an equation:

0.75x = 600

To find x, divide both sides of the equation by 0.75:

x = 600 / 0.75

x = 800

As a result, the bookstore had 800 books before the holiday.

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Answer:

Other leg: 25 cm

Hypotenuse: 25√2 cm

Step-by-step explanation:

Hi there!

We are given a 45°-45°-90° triangle, and one leg (a side that makes up the right triangle) measures 25 cm

We want to find the length of the other sides

First, let's find the length of the other leg

A 45°-45°90° triangle is actually an isosceles triangle, and if it was to be drawn, the base angles are 45 and 45 degrees

That means the legs of the right triangle are actually the legs in the isosceles triangle as well

So the other leg is also 25 cm

Now, let's find the length of the hypotenuse, which is the side OPPOSITE from the 90° angle

You can solve for the other side using Pythagorean Theorem if you wish, however, there is a shortcut to finding the hypotenuse

In a 45°-45°-90° triangle, if the length of the legs are a, then the hypotenuse is a√2 cm

So that means the length of the hypotenuse in this case is 25√2 cm

Hope this helps!

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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Answer:

x<9

Step-by-step explanation:

so first you add 4 to both sides,

then it is x<9 right?

WELL THAT'S THE ANSWER :)

pls give me brainliest

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THEY ARE CORRECT

GIVE THEM BRAINLIST BEFORE THIS GETS DELETED

Answer:

Based on the given conditions, formulate:

238

−

144

Calculate the sum or difference:

94

get the result:

94

Answer: Step-by-step explanation:

Answer:

it would be y= 3/4x + 2

Step-by-step explanation:

the form is y=mx+b

and you have to set it up as 8y=16-6x

Divide each term

Cancel the common factor of 8.

Divide y by 1

then simplify and turn it into a fraction.

Answer:28.16

Step-by-step explanation:

A markup of 220% would bring 11 to 35.20, and a mark down of 20% would bring 35.20 to 28.16.

Your'e Welcome  (ФДФ) .

Answer:

3w + 25m = T

i think-

[MA]:

3w + 25m = T

Writer's note: I'm not sure if this is really correct.

[xArtsy]