Using Functions Notation
Given the following functions:
f(n) = 2n + 3, g(n) = n³ + 4
Find the following:
f(4) - f(2)

Answer:

Step-by-step explanation:

let numerator=x

denominator=x+3

again

[tex]\frac{x+2}{x+3+2} =\frac{2}{3} \\3(x+2)=2(x+5)\\3x+6=2x+10\\3x-2x=10-6\\x=?[/tex]

x=4

number is

[tex]\frac{4}{4+3} \\=\frac{4}{7}[/tex]

The amount withheld in FICA Tax for Sol Berenson's weekly earnings is given as follows:

$749.7.

To calculate the amount withheld by Berenson's employer in FICA tax, we apply the proportion of the FICA tax to his total earnings.

Researching on a web search, the FICA tax rate is given as follows:

15.3% = 0.153.

As the FICA tax is a combination of the Medicare tax with the Social Security tax.

Sol Berenson's gross weekly earnings are given as follows:

$4,900.

(as stated in the problem).

The amount withheld is 15.3% of that, which is found applying the proportion, which is the multiplication of 0.153 by 4900 as follows:

Amount Withheld = 0.153 x 4900 = $749.7.

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The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = [tex]C(n , k) * p^k * (1 - p)^{(n - k)}[/tex]

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = [tex]C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}[/tex]

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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Here, we must use one sample z test for the first question.

Since the population standard deviation is known in this instance. According to the new protein powder firm, it takes an average of 7 days to add 10% more muscle, with a population standard variation of 5.5 days.

Here, keep in mind that the t test should be used if the population standard deviations are unknown and the z test should be used if the population standard deviations are known.

The second question requires that we test the hypothesis to determine whether the MoCA test differs between the days before and after several exposures to a new tool.

Here, a z-test with two samples was utilized. Once the hypothesis has been stated, the z Statistic

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The required values of functions (f₀g)(-3) is 11 and (g₀f)(6) is 23 respectively.

What is a function?

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).

Given, f(x) = 4x - 1

g(x) = |x|

a) (f₀g)(-3) = f(g(-3)) = f(|-3|) = f(3) = 4*3-1 = 11

b) (g₀f)(6) = g(f(6)) = g(4*6-1) = g(23) = 23

Hence, the required values of functions (f₀g)(-3) is 11 and (g₀f)(6) is 23 respectively.

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Answer: P/2 - L = W

Step-by-step explanation:

P = 2L + 2W. We are isolating W. Subtract 2L from both sides to isolate the term first
P - 2L = 2W. Divide by 2 on both sides to isolate W.
P/2 - L = W

Answer:

4

Step-by-step explanation:

Answer:

The rate of change is 4

Step-by-step explanation:

The rate of change is the slope.

Since the equation is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 4x-3

The slope is 4 and the y intercept is -3

Answer:

final answer would be $6,550

Step-by-step explanation:

To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:

Income Range: $0 - $10,000

Progressive Tax Rate: 3%

Tax Owed: $0 - $10,000 * 3% = $0 - $300

Income Range: $10,001 - $50,000

Progressive Tax Rate: 5%

Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500

Income Range: $50,001 - $100,000

Progressive Tax Rate: 5.5%

Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500

Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.

The required, subtraction of 7x-9 from 2x² - 11 is 2x²-7x-2. Option B is correct.

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

Here,

To subtract 7x-9 from 2x² - 11, we need to distribute the negative sign across 7x and 9, and then combine like terms.

=2x² - 11 - (7x - 9)

= 2x² - 11 - 7x + 9

= 2x² - 7x - 2

Therefore, the answer is 2x²-7x-2.

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Yes, the condition that X is normally distributed is satisfied. When a simple random sample is drawn from a population that is normally distributed, the sample will also be normally distributed, as long as the sample size is large enough (generally considered to be at least 30 observations). In this case, the sample size of 36 observations is sufficient to ensure that the sample is normally distributed.

The standard deviation is a useful measure because it allows you to compare the spread of different data sets, even if they have different means. For example, if two data sets have the same mean but one has a larger standard deviation, this suggests that the values in the data set with the larger standard deviation are more spread out or variable.

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Answer: i think 15/8 but, im not sure

Step-by-step explanation:

We get the following answers;

(a) The necessary histogram has been created and is supplied below.

(b) According to the data, it is indeed dangerous to drive close to home. Because 23% and 29% of accidents occur within 1 to 5 miles of home, respectively.

Step 1: in 2001, progressive insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. the data are summarized in the table.

Step 2:

Table :

Miles from home          % of accidents      Cumulative

Less than 1                               23                        23

1 to 5                                         29                        52

6 to 10                                       17                         69

11 to 15                                       8                          77

16 to 20                                     6                         83

over 20                                     17                        100

(a) the required histogram is made and attached below.

(b) Yes, the data indicates that driving near home is particularly dangerous. Because, less than , 1 to 5 miles from home 23%, 29% of accidents.

Hence we get the required answers.

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Sales of one store is $274762500 and sales of other store is $275237500.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Given

In a recent year, the total sales at Restaurant A were $475,000 more than at Restaurant B. Total sales at the two stores were $550,000,000.

Let sales of one store be x

Equation,

475000 + x + x = 550,000,000

2x = 550,000,000 - 475000

2x = 549525000

x = 274762500

Sales of one store = $274762500

Sales of other store

= $274762500 + $475000

= $275237500

Sales of one store is $274762500 and Sales of other store is $275237500.

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An expression which describe the given sequence is, an = -2 + n.

Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.

an = -2 + n is an expression which describe the given sequence

The general rule for the arithmetic sequence is given by,

 an = a + (n - 1)d  ......[1]

where, denotes the initial word.

the common difference

there are n terms;

The given order is -1, 0, 1, 2,.....

This is a frequent difference arithmetic sequence.

Since,0-(-1) = 1

1-0 =1

2-1 = 1 ....

Here, a1 = -1

When you replace [1] with the value of d = 1, you get, a1 = -1

an = -1 + (n -1)(1)

an = -2 + n

Consequently, the following expression describes the given sequence: an = -2+n.

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Answer:

first option

Step-by-step explanation:

using the property of logarithms

ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )

given

[tex]17^{(0.3x+5)}[/tex] = 12

take the ln of both sides

ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then

(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )

0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )

0.3x ≈ - 4.12293 ( divide both sides by 0.3 )

x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )

Answer:

p = 72

Step-by-step explanation:

If we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.

4 × y =?

5 × y =?
We need to put a value in for y.

Let's use 9.

4 × 9 = 36 (P)

5 × 9 = 45 (Q)

Now let's add 12 to P, and take away 6 from Q.

36 + 12 = 48

45 - 6 = 39

The numbers aren't the same yet.

Let's use a different value for y.

y = 18

The equations will now look like this:

4 × 18 = 72 (P)

5 × 18 = 90 (Q)

Let's add 12 and 6 to the numbers again.

72 + 12 = 84

90 - 6 = 84

The numbers match up!

Therefore, the original price of p = 72

third side,  AB= 14.318 Units  and  tanB = 0.461

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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Using Pythagoras theorem, Third side,  AB= 14.318 Units  and tanB = 0.461

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

given:

BC=13 units

AC=6 units

solution:

using pythagoras theorem, we get

AB² = BC² + AC²

AB² = 13² + 6²

AB² = 169 + 36

AB² = 205

AB = 14.318 units

tanB = side opposite/side adjacent

tanB = AC/BC

tanB = 6/13

tanB = 0.461

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The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)

The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,

Abd here we must have to find the linear constraint of the form of the variables.

While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.

And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.

Here the term of blend refers the sum of the terms,

Then the linear constraint form of the variables is written as,

=> X1 =< 0.75 (X1 + X2 + X3)

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A Confidence Interval shows the joint or bivariate relationship between two categorized (nominal and/or ordinal) variables.

Data that is labeled without using quantitative data is known as nominal data.

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number.

A variable is categorical unless it has a numerical value, in which case it is referred to as a quantitative variable.

The category and quantitative variables are now classified as follows:

Duration is a quantitative variable with interval as its unit of measurement.

Ratings are categorical variables with an ordinal level of measurement.

The degree of measurement for the categorical variable "voting status" is nominal.

Ordinal data are those that can be arranged.

The highest and smallest known values are continuous and discrete values for interval data, respectively. The order is clear here. Here, the distinction between two values means something.

All of the characteristics of interval data apply to ratio data, plus it has the definition of zero(0), meaning that no points are included. For instance, height, weight, etc.

Because ratio includes both continuous and discrete data, it is likely that the difference between any two numbers won't be the same.

It is interval data since everyone knows when a class starts and when it ends, and it also has these two times. for instance, between 9:00 to 10:00

Nominal because the information is categorical.

Ordinary, given that we may get quality products here. Good, acceptable, or poor.

Ordinal because the marks can be arranged.

Ordinary since we can arrange the ages.

Line symmetry; rotational symmetry; the reflection in the line x = 0, the reflection in the line y = 0 the reflection in the line y = x and the reflection in the line y = -x map the square onto itself; the rotations of 90°, 180°, 270° and  around the point ( 0 , 0 ) map the square onto itself.

Therefore,

A Confidence Interval shows the joint or bivariate relationship between two categorized (nominal and/or ordinal) variables.

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In response to the question, we may say that As a result, the right answer  expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.

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.

To carry out the random assignment, we may utilise the following table of random digits:

Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.

Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.

We can get the following random assignment using this method:

A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9

As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.

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Answer:

A: 0, 7, 5, 8, 1  B: 3, 4, 2, 6, 9

Step-by-step explanation:

THE ANSWER IS D

Answer:

Step-by-step explanation:

3x^2 = -12

x^2 = -4

x = ±√-4

this equation has no real solutions

Answer:

-------------------------------

The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.

Probability

A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.

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The length of EF in line segment DF is 15.

A line segment's boundaries are two separate places on the same line. Another way to describe a line segment is as a piece of the line that joins two points.

Given that,

Length of line segment DF = 19.

Also, E is any point on line segment,

And DE = 4.

To find the length of EF,

Since, E lies on line segment DF,

Implies that,

DE + EF = DF

4 + EF = 19

EF = 15

The required length of EF is 15.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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Answer:

f(-5) = -9

Step-by-step explanation:

f(x) = 2x + 1

f(-5) = 2(-5) + 1

f(-5) = -10 + 1

f(-5) = -9

The number of meals that Boris can feed his dog will be 50 meals.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Boris takes care of his canine with 3/5 pounds of canine nourishment for every dinner. Boris has quite recently purchased 30 pounds of canine food.

The number of meals that Boris can feed his dog will be calculated as,

⇒ 30 ÷ (3/5)

Simplify the expression, then we have

⇒ 30 ÷ (3/5)

⇒ 30 / (3/5)

⇒ 30 x 5 / 3

⇒ 10 x 5

⇒ 50

The number of feasts that Boris can take care of his canine will be 50 dinners.

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Answer: B

Step-by-step explanation:

The two equations have the same slope, but different points. This means that the lines are parallel to one another and will not intersect.

The answer is B: No solution

Answer: No solution.

Step-by-step explanation: I graphed the two given functions below.  It looks like there is no solution to the given functions.

Hope this helps! :)

Answer:

0.25

Step-by-step explanation:

Step 1: Convert all fractions to decimals

Two-thirds = 0.6666

Three-quarters = 0.75

One-half = 0.5

Step 2: Multiply all fractions

0.6666 * 0.75 * 0.5 = 0.25

Step 3: The answer is 0.25

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Three-quarters of one half:

[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]

Two-thirds of "Three-quarters of one half":

[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]

Answer:

Step-by-step explanation:

You want the value of x that makes the perimeter of a rectangle be 38 cm when sides are x and (2x+7). And you want the largest angle in the quadrilateral with angles x+17, 2x+15, 2x+30, and 4x+19.

The perimeter of a rectangle is given by the formula ...

  P = 2(L +W)

Substituting the given values, we have ...

  38 = 2((2x+7) +x)

Dividing by 2 gives ...

  19 = 3x +7

  12 = 3x . . . . . . . subtract 7

  4 = x . . . . . . . divide by 3

The value of x is 4 cm.

The sum of the angles of a quadrilateral is 360°. This tells us ...

  360 = (x +17) +(2x +15) +(2x +30) +(4x +19)

  360 = 9x +81 . . . . . . . collect terms

  40 = x +9 . . . . . . divide by 9

  31 = x . . . . . . . subtract 9

The largest angle is 4x+19, or 4(31) +19 = 124 +19 = 143.

The largest angle is 143°.

Answer:

The answers are attached to this response.

Step-by-step explanation:

1.

⭐Properties of a rectangle

Using the properties of a rectangle, let's form an equation of the perimeter to solve for x.

perimeter = 2(length) + 2(width)

38 = 2(2x+7) + 2(x)

38 = 4x + 14 + 2x . . . . . . . . .  distribute the coefficients of the expressions

38 = 6x + 14 . . . . . . . . . . . . .  add like terms

24 = 6x . . . . . . . . . . . . . . . . . subtract 14 from LHS and RHS

∴ 4 = x . . . . . . . . . . . . . . . . . . divide LHS and RHS by 6

2.

The figure shown makes the shape of a kite.

⭐Properties of a kite

Using the properties of a kite, let's form an equation of the sum of the internal angles  to solve for x, and then substitute x into the largest angle expression to find its angle measure.

(∠1) + (∠2) + (∠3) + (∠4) = 360°

(2x + 15) + (2x+30) + (4x+19) + (x+17) = 360

9x + 81 = 360 . . . . . . . add like terms

9x = 279 . . . . . . . . . . . subtract 81 from LHS and RHS

x = 31 . . . . . . . . . . . . . . divide LHS and RHS by 9

Substitute x into the largest angle expression to find its angle measure.

4(31) + 19 = 143°

∴ 143° is the largest angle