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Part 1
The functions f and g are defined as
​f(x)=7x
and
​g(x)=x−5.
​a) Find the domain of​ f, g,
f+​g,
f−​g,
​fg, ff,
fg​,
and
gf.
​b) Find
​(f+​g)(x),
​(f−​g)(x),
​(fg)(x), (ff)(x),
fg(x)​,
and
gf(x).

The inverse of the function f(x) = x² + 3 is, f⁻¹(x) = ± √(3 - x) and it is not a function.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, A function f(x) = x² + 3.

Let, y = x² + 3.

x² = 3 - y.

x = ± √(3 - y).

f⁻¹(x) = ± √(3 - x).

The inverse of the function is not a function as two distinct outputs have the same intput.

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a) is linearly dependent and set b) is linearly independent.

By inspection, we can determine whether the given sets are linearly dependent by looking at the relationship between the vectors in each set. If one vector can be written as a linear combination of the other vectors in the set, then the set is linearly dependent.

For set a) \( \left\{\left[\begin{array}{l}1 \\ 3\end{array}\right],\left[\begin{array}{l}2 \\ 6\end{array}\right]\right\} \), we can see that the second vector is simply 2 times the first vector. This means that the second vector can be written as a linear combination of the first vector, and therefore the set is linearly dependent.

For set b) \( \left\{\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right],\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right],\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]\right\} \), we can see that none of the vectors can be written as a linear combination of the other vectors in the set. This means that the set is linearly independent.

Therefore, by inspection, we can determine that set a) is linearly dependent and set b) is linearly independent.

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The variance of the sample of data is 3.33.

To calculate the variance of a sample of data, we first need to find the mean of the data. The mean is the average of all the data points.

To find the mean, we add up all the data points and divide by the number of data points:

(7 + 5 + 8 + 4 + 6 + 3 + 9 + 7 + 6 + 5) / 10 = 60 / 10 = 6

Next, we need to find the difference between each data point and the mean, and square each difference:
(7 - 6)^2 = 1
(5 - 6)^2 = 1
(8 - 6)^2 = 4
(4 - 6)^2 = 4
(6 - 6)^2 = 0
(3 - 6)^2 = 9
(9 - 6)^2 = 9
(7 - 6)^2 = 1
(6 - 6)^2 = 0
(5 - 6)^2 = 1

Next, we add up all the squared differences:

1 + 1 + 4 + 4 + 0 + 9 + 9 + 1 + 0 + 1 = 30

Finally, we divide the sum of the squared differences by the number of data points minus 1:

30 / (10 - 1) = 30 / 9 = 3.33

Therefore, the variance of the sample of data is 3.33.

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There are a total of 26 letters in the English alphabet and 10 digits (0-9). Therefore, the total number of car number plates that can be made if each plate contains 3 different letters followed by 3 different digits can be calculated as follows:

- For the first letter, there are 26 options.

- For the second letter, there are 25 options (since the first letter has already been used).

- For the third letter, there are 24 options (since the first and second letters have already been used).

- For the first digit, there are 10 options.

- For the second digit, there are 9 options (since the first digit has already been used).

- For the third digit, there are 8 options (since the first and second digits have already been used).

Therefore, the total number of car number plates that can be made is:

26 × 25 × 24 × 10 × 9 × 8 = 11,232,000

So, the answer is 11,232,000 car number plates can be made if each plate contains 3 different letters followed by 3 different digits.

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We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:

8 individuals per boat times 1,254 passengers is 156.75 boats.

We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

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Answer:

The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

6th line: 2(x) - 1 (unknown)

To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:

2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)

2x - 1 = 33

2x = 34

x = 17

Therefore, the 6th line of the pattern would have 17 marbles

Step-by-step explanation:

The pattern is described as having a number in each line that is one less than twice the previous line.

Write out the first few lines of the pattern, starting with 2 as the first line:

1st line: 2

2nd line: 2(2) - 1 = 3

3rd line: 2(3) - 1 = 5

4th line: 2(5) - 1 = 9

5th line: 2(9) - 1 = 17

To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:

6th line: 2(x) - 1

Substitute 17 for x (the value in the 5th line):

2(x) - 1 = 2(17) - 1

Simplify the right-hand side:

2(x) - 1 = 33

Add 1 to both sides:

2(x) = 34

Divide both sides by 2:

x = 17

Therefore, the 6th line of the pattern would have 17 marbles.

The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.

To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.

Starting with two, we can apply the rule to generate the next few numbers:

First line: 2

Second line: 2(2) - 1 = 3

Third line: 2(3) - 1 = 5

Fourth line: 2(5) - 1 = 9

Fifth line: 2(9) - 1 = 17

Now we can apply the rule again to find the sixth number:

Sixth line: 2(17) - 1 = 33

Therefore, the sixth line must have 33 marbles.

The pattern starts with two, which is the first line.

The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.

To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.

Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.

We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.

Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.

So, the complete pattern is: 2, 3, 5, 9, 17, 33.

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The surface area of the cylinder with a radius of 1 ³/₄ and height of 3 ¹/₄ units will be 35.72 square units.

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πrh square units

The radius is 1 ³/₄ units and the height is 3 ¹/₄ units.

First, convert the mixed fraction number into a fraction number. Then we have

1 ³/₄ = 7/4 units

3 ¹/₄ = 13/4 units

The surface area of the cylinder is calculated as,

SA = 2 x 3.14 x (7/4) x (13/4)

SA = 35.72 square units

The surface area of the cylinder with a radius of 1 ³/₄ and height of 3 ¹/₄ units will be 35.72 square units.

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The complete question is given below.

Exact surface area. The radius is 1 3/4 and the height is 3 1/4 of the cylinder.

The combination that is produced contains 57.5% corn.. It is calculated by taking the weighted average of the corn content in the two bags, accounting for their respective weights.

(50% x 20 lbs) + (65% x 30 lbs)

= 1750 lbs + 1950 lbs

= 3700 lbs

3700 lbs/50 lbs

= 57.5%

The concentration of corn in the resulting mixture is 57.5%. This is calculated by taking the weighted average of the corn content in the two bags. The first bag, containing 20 pounds of calf starter mix, contains 50% corn. The second bag, containing 30 pounds, contains 65% corn. To calculate the concentration of corn in the mixture, the percentage of corn in each bag is multiplied by its respective weight, and the sums of these two products are then divided by the sum of the two weights. In this case, (50% x 20 lbs) + (65% x 30 lbs) = 1750 lbs + 1950 lbs = 3700 lbs. The resulting concentration of corn in the mixture is 3700 lbs/50 lbs = 57.5%.

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Answer: G=(3, 4) R=(4, 8) A=(7, 8) M=(6, 4)

Step-by-step explanation:

translation is the movement of a point so 11 units right add 11 to the x value and 2 to the y value then do the opposite for going left and down

The vectors [tex]([1],[-2],[3]),([2],[-2],[0])[/tex] and [tex]([0],[1],[7])[/tex] are a linearly independent set.

To determine if the vectors are a linearly independent set, we can use the determinant method. The determinant of a 3x3 matrix is given by:

[tex]\begin{bmatrix}a_1 & a_2 &a_3 \\  b_1& b_2 &b_3 \\  c_1&c_2  &c_3 \end{bmatrix}[/tex]

We can create a 3x3 matrix using the given vectors as the columns of the matrix:

[tex]\begin{bmatrix}1 & 2 &0 \\  -2& -2 &1 \\  3&0  &7 \end{bmatrix}[/tex]

Now, we can find the determinant of this matrix using the formula:

[tex]det(\begin{bmatrix}1 & 2 &0 \\  -2& -2 &1 \\  3&0  &7 \end{bmatrix})[/tex]

[tex]= 1(-2*7 - 1*0) - 2(-2*7 - 1*3) + 0(-2*0 - 1*-2)[/tex]

[tex]= -14 - 0 - 4(-14) - 6 + 0[/tex]

[tex]= -14 + 56 - 6[/tex]

[tex]= 36[/tex]

Since the determinant is not equal to zero, the vectors are linearly independent.

Therefore, the vectors[tex]([1],[-2],[3]),([2],[-2],[0])[/tex] and [tex]([0],[1],[7])[/tex] are a linearly independent set.

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The figure represented here is a square pyramid.

With a square base and fοur triangular sides that are cοnnected at a vertex, a square pyramid is a three-dimensiοnal geοmetric οbject. It has a pentahedrοn shape with five faces.

Fοur triangles are jοined at each vertex tο a square fοundatiοn tο fοrm a square pyramid. It has a square fοundatiοn, and triangles with a shared vertex make up its side faces.

We can get the squared pyramidal figure by fοlding the triangles οf equal size frοm all the sides.

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Answer:

To find the value of b x6 when b = 7, we simply need to substitute 7 for b in the expression and perform the multiplication.

b x 6 = 7 x 6

Multiplying 7 by 6 gives us:

b x 6 = 42

Therefore, when b = 7, the value of b x 6 is 42.

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7527861800

Answer:

Step-by-step explanation:

Let [tex]x[/tex] be number of $1 bills.

Let [tex]y[/tex] be the number of $5 bills.

So we get:

[tex]x+y=60[/tex]       [tex](1)[/tex]

[tex]x+5y=150[/tex]   [tex](2)[/tex]

Then we solve these simultaneously:

[tex](2)-(1)[/tex]  gives

[tex]4y=90[/tex]  ⇒ [tex]y=22.5[/tex]

Substitute [tex]y=22.5[/tex] into [tex](1)[/tex] gives:

[tex]x+22.5=60[/tex]  ⇒  [tex]x=37.5[/tex]

So there appears to be no solution to this question as you cannot have half bills.

The uncertainity for the meter stick and weights in this experiment are σₓ =  σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg), respectively.

This means that the uncertainty in the measurement of the meter stick is 1 × 10⁻³ meters and the uncertainty in the measurement of the weights is 0.05 kg. To calculate the uncertainity of the results, one must use the appropriate formulae, taking into account the uncertainities of each measurement.

For example, if you are measuring the mass of an object, you must use the uncertainty in the measurement of the weight and the uncertainty in the measurement of the meter stick to calculate the uncertainty in the mass.

The uncertainty in the mass is then equal to the square root of the sum of the squares of the uncertainties of the measurements.

By taking into account the uncertainties in each measurement, one can accurately calculate the uncertainty of the results.

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Complete question:

In this experiment you can use  σₓ =  σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg)  as the uncertainity for the meter stick and weights, respec.

The standard form to this equation is x=2/3.

This equation is in the form of a linear equation in one variable, where the variable is x.

The equation is written as x=2/3, meaning that the value of x is equal to 2/3.

The equation can be interpreted as the ratio of two numbers, 2 and 3. The numerator, 2, represents the number of parts, and the denominator, 3, represents the total number of parts.

This equation can be used to solve for the fraction of the total number of parts represented by the numerator. In this case, the fraction is 2/3, or 2 parts out of a total of 3 parts.

The equation can also be interpreted as a proportion. If we make the numerator the unknown value, x, then the equation becomes x/3 = 2/3. This equation can be solved using the cross-multiplication method.

By multiplying the denominators together and setting them equal to each other, then solving for x, we get x = 2/3. This equation shows that the value of x is equal to 2/3 of the total number of parts.

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Answer:

Two possible answers: 36 and 4m

Step-by-step explanation:

Changes is not specific, but we know it is a vertical change due to it saying elevation.

20+16=36m

20-16=4m

We don't know if the bird is going up or down.

Down is 4m and up is 36m

The value of m∠A + m∠B is 90°. The angles that add up to 180 degrees are referred to as supplementary angles.

Option C is correct.

Given a figure, we must determine the sum of the angles A and B. The angle that forms a linear pair with the sum of the angles A and B is 90 degrees. Since we are aware that the linear pair with a 90 degree angle is 90 degrees, the value of the sum of the angles A and B, m  A + m  B, is also 90 degrees.

There can be no more than three angles. Two angles whose measurements add up to exactly 180 degrees are referred to as supplementary angles. It is possible to have three angles that add up to 180 degrees each, such as 60 degrees, 30 degrees, and 90 degrees; however, these angles are not considered supplementary.

Question incomplete:

What is the value of m∠A + m∠B? If ∠ C = 56° and ∠D =124°

A. 180

B. 120

C. 90

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If the dividend is 872 and the quotient is 62 and remainder is 4, the divisor is equal to 14.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

In Mathematics, dividend can be calculated by using this mathematical expression:

Dividend = divisor × quotient + residual

Substituting the given data points into the dividend formula, we have the following;

Dividend = divisor × quotient + residual

872 = divisor × 62 + 4

Divisor = (872 - 4)/62

Divisor = 868/62

Divisor = 14

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Complete Question;

If the dividend is 872 and the quotient is 62 and remainder is 4. What is the divisor?

Triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.

In geometry, two triangles are said to be congruent if they have the same shape and size. More specifically, two triangles are congruent if all three sides and all three angles of one triangle are equal to the corresponding sides and angles of the other triangle. When two triangles are congruent, they can be superimposed on top of each other, and all corresponding parts of the triangles will match exactly.

There are several ways to prove that two triangles are congruent, including using the side-angle-side (SAS) theorem, the angle-side-angle (ASA) theorem, the side-side-side (SSS) theorem, and the hypotenuse-leg (HL) theorem.

Given that |AB|=|CD| and triangle ABC is isosceles.

We need to prove that triangle AXC = triangle AYB.

To do so, we will use the Side-Angle-Side (SAS) Congruence Criteria.

AC = BC (Given)

∠ACX = ∠BCY (Vertical Angles)

∠CAX = ∠CBY (Base Angles of Isosceles Triangle)

Therefore, triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.

Hence, proved.

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Answer:

60

Step-by-step explanation:

850-250=600

600/10=60

60

Answer:

she must save $60 each week to have enought money to purchase the iPhone 10

Step-by-step explanation:

Because 850-250=600

                 600/10=60                

The first set is countable, the second set is also countable. The third set is also countable.

(a) The set {x∈R:2 is countable because it is finite.
(b) The set {x∈Q:∣x∣≥2} is countable because it is a subset of the rational numbers, which are countable.
(c) The set {x∈Q:∣x∣<4} is countable because it is a subset of the rational numbers, which are countable.

In Maths, sets are referred as a collection of well-defined objects or elements. A set is usually represented by a capital letter symbol and the total number of elements in the finite set is basically represented as the cardinal number of a set in a curly bracket.

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In regards to question A:

P(G) = 0.2

P(W) = 0.32

P(B) = 0.48

B: we can estimate that the friends will choose approximately 90 glass beads, 144 wood beads, and 216 brass beads if they select a total of 450 beads from the crate.

a. The probability model for choosing a bead can be represented by a discrete probability distribution, where the sample space consists of the three types of beads - glass, wood, and brass - and the probabilities of selecting each type are proportional to their respective frequencies. Let P(G) denote the probability of selecting a glass bead, P(W) denote the probability of selecting a wood bead, and P(B) denote the probability of selecting a brass bead. Then:

P(G) = [tex]\frac{60}{300}[/tex] = 1 ÷ 5 = 0.2

P(W) = [tex]\frac{96}{300}[/tex] = 8 ÷ 25 = 0.32

P(B) = [tex]\frac{144}{300}[/tex] = 12÷ 25 = 0.48

b. To estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate, we can use the probabilities calculated above to find the expected number of beads of each type. Let X_G, X_W, and X_B denote the random variables representing the number of glass, wood, and brass beads, respectively, that are selected out of the 450 total selections. Then:

E(X_G) = P(G) × 450 = (1 ÷ 5) × 450 = 90

E(X_W) = P(W) × 450 = (8 ÷ 25) × 450 = 144

E(X_B) = P(B) × 450 = (12 ÷ 25) × 450 = 216

Therefore, based on the frequencies in the table, we would expect approximately 90 glass beads, 144 wood beads, and 216 brass beads to be chosen if the friends select a total of 450 beads from the crate.

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The value of a is 20, b is 40, c is 10 and d is 10√3

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

By using sine function we find the value of a

sin 45=a/20√2

1/√2 = a/20√2

20√2=a√2

a=20

Now let us find c

cos 45=c/(20√2)

1/√2×20/√2=c

10=c

sin30=a/b

1/2=20/b

b=40

Now we have to find d by cosine function

cos30=d/a

√3/2=d/20

d=10√3

Hence, the value of a is 20, b is 40, c is 10 and d is 10√3

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Answer:

[tex]\boxed{R:-40.48}[/tex]

Step-by-step explanation:

Rewriting the statement we have:

[tex]-44+22 \times\frac{ 16}{100}[/tex]

According to the order of operations, we solve:

simplify:

[tex]-44+22 \times\frac{ 4}{25}\\=-44 +\frac{88}{25} \\=\frac{-44(25)+88}{25} = \frac{-1012}{25} \approx -40.48[/tex]

Length of the side of square is x = 5.7 unit

The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base and the hypotenuse. Here, the hypotenuse is on the opposite side of the 90° angle, so it is the longest side.

Given,

Figure of a rectangle and a right triangle share its hypotenuse with length of rectangle

diagonal of rectangle = 8

length of both sides of right triangle other than hypotenuse = 4

Let length of rectangle be l

By Pythagoras theorem

l² = 4² + 4²

l² = 32

l = 4√2

Now, In the rectangle

8² = l² + x²

64 = 32 + x²

x² = 32

x = 4√2

x = 5.7

rectangle is an square.

Hence value of x, length of the side of square is 5.7 unit.

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Answer: 3.25h + 12= 9.25

Step-by-step explanation:

12 is the initial fee which we will just add to our answer

3.25 is the rate per hour, it is being multiplied by the number of hours.

the number of hour it took to reach the same cost is not told so we will just put a variable.

Alisha's total earnings for the week would be $650.

Why it is and what is selling?

Alisha's total earnings for the week can be calculated as follows:

Commission earned on sales = 15% of $2000 = 0.15 x $2000 = $300

Total earnings for the week = Base salary + Commission earned

= $350 + $300

= $650

Therefore, Alisha's total earnings for the week would be $650.

Selling refers to the exchange of goods or services for money or other valuable consideration. It is the process of convincing or persuading potential customers to purchase a product or service. Selling involves various activities, including advertising, marketing, negotiating, and closing a sale.

The goal of selling is to create a relationship with the customer that leads to repeat business and referrals. It is an essential aspect of commerce and business, as it generates revenue and helps companies grow and expand.

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To determine how much greater the fractional part of a college student's daily servings that comes from grains than from fruits, we would need to know the specific fractions or percentages of each type of food that the student consumes. Without this information, it is impossible to accurately answer the question.

For example, if the student consumes 1/2 of their daily servings from grains and 1/4 of their daily servings from fruits, then the difference would be 1/2 - 1/4 = 1/4 or 25%. However, without knowing the specific fractions or percentages, we cannot determine the difference.

It is important to remember that a balanced diet should include a variety of food groups, including grains, fruits, vegetables, proteins, and dairy. The specific amounts of each will vary depending on individual dietary needs and preferences.

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