Determine whether f(x)=x9+43
and g(x)=9x+12
are inverses. Explain your reasoning.

Answer:

Step-by-step explanation:

7 + 3 ( v - 2u )/u + 1

u = 2 and v = 5

7 + 3(v - 2u)/u + 1

7 + 3 ((5) - 2(2)) / (2) + 1

→ 7+3 ((5) -2 (2)) = 10

→ (2) + 1  = 3

10/3

Answer:

10/3

Step-by-step explanation:

u = 2

v = 5

7 + 3(v - 2u)

= 7 + 3(5 - 2*2)

= 7 + 3(5 - 4)

= 7 + 3(1)

= 7 + 3

= 10

u + 1

= 2 + 1

= 3

7 + 3(v - 2u)/u + 1

= 10/3

Answer:

if we substitute x = 3 in the given function f(x) = r + 7, we get:

f(3) = r + 7 (where x = 3)

Therefore, the value of f(3) is r + 7.

The correct answer is option A. 2.5.

What is a number line?

A number line is a visual representation of a line where the points are the real numbers. The line is usually drawn horizontally, with zero in the center and positive numbers to the right and negative numbers to the left. The numbers on the number line are evenly spaced and correspond to points on the line. A number line is a useful tool for understanding the relationships between numbers and for performing operations such as addition and subtraction. It is also used to represent measurements, such as distances and time intervals.

To find the midpoint of a line segment, we add the coordinates of the two endpoints and divide by 2. In this case, the coordinates of point S are -2 and the coordinates of point T are 7.

So the coordinate of the midpoint, point R, is:

R = (S + T)/2 = (-2 + 7)/2 = 5/2 = 2.5

Therefore, point R lies at 2.5 on the number line.

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Answer:

We can use the Pythagorean theorem to determine if the triangle is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as a = 18 mm, b = 25 mm, and c = 15 mm. We want to see if a right angle exists between sides a and b, so we will check if c² = a² + b².

a² + b² = 18² + 25² = 324 + 625 = 949

c² = 15² = 225

Since c² is not equal to a² + b², the triangle is not a right triangle.

Therefore, the answer is no, the triangle is not a right triangle.

Answer:

To write the ratio 3.0 to 1.2 in lowest terms using a colon, we need to divide both numbers by their greatest common factor (GCF).

The GCF of 3.0 and 1.2 is 0.6, since:

3.0 = 5(0.6)

1.2 = 2(0.6)

Dividing both numbers by 0.6, we get:

3.0/0.6 = 5

1.2/0.6 = 2

Therefore, the ratio 3.0 to 1.2 in lowest terms using a colon is:

5:2

Answer:

Total Charge = Initial Charge + Daily Charge x Number of Days

Step-by-step explanation:

Let's assume that x is the number of days that Frank rented the car.

The initial charge for the rental is $40, which is a one-time charge, so it does not depend on the number of days.

The daily charge for x days is $35 per day. Therefore, the total charge for x days can be calculated as:

Total Charge = Initial Charge + Daily Charge x Number of Days

Total Charge = $40 + $35x

We know that Frank was charged $180, so we can set the total charge equal to $180 and solve for x:

$40 + $35x = $180

Subtracting $40 from both sides gives:

$35x = $140

Dividing both sides by $35 gives:

x = 4

Therefore, Frank rented the car for 4 days.

The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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The equation of g ( x ), given that it is a vertical stretch, would be (4/5)x² - 4.

The output (dependent variable) of f(x) must be multiplied by the stretching factor in order to obtain the equation of g(x), which is a vertical stretching of f(x) by a factor of 2.

The function can be shown as:
f(x) = Ay² + B

g(x) = 2(Ay² + B)

g(x) = 2((2/5)x² - 2)

g(x) = (4/5)x² - 4

So, the equation of g(x) is g(x) = (4/5)x² - 4.

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The probability for each colour of the block is removed from the box is as follows:

Blue: 9/40

Red: 15/40

Yellow: 11/40

Orange: 5/40

Explain the term probability

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. It is used to model uncertainty and randomness in various fields, such as statistics, science, engineering, and economics. Probability theory provides a framework for analyzing and predicting the outcomes of random experiments, and it has applications in many real-world situations, such as gambling, insurance, and quality control.

According to the given information

The probability of drawing a block of a certain colour from the box can be calculated by dividing the number of blocks of that colour by the total number of blocks in box 1. Based on the experimental results, the probability for each color of block being removed from the box is as follows:

The probability of drawing Blue: 9/40

The probability of drawing Red: 15/40

The probability of drawing Yellow: 11/40

The probability of drawing Orange: 5/40

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Answer:

First, we need to figure out how many socks are in the drawer.

5 black socks + 5 striped socks + 9 polka dot socks + 11 white socks + 5 blue socks + 1 sock with photos of small socks = 36 socks

Pay attention to the polka dot socks now. There are 9 polka dot socks in the drawer; the odds of picking one on the first draw are 9/36 socks.

If we don't replace the first sock and draw again, there will be 8 polka dot socks remaining out of a total of 35 socks in the drawer.

As a result, the likelihood of picking a second polka dot sock after selecting the first is 8/35.

To calculate the likelihood of picking a pair of polka dot socks, multiply the odds of selecting a polka dot sock on the first draw by the probability of selecting another polka dot sock on the second draw.

The probability of choosing a pair of polka dot socks is (9/36) x (8/35) = 0.0571, or approximately 5.71%.

The z score that corresponds to P4 is = -1.75

let the z score corresponding to the 4th percentile be a.

according to the problem:-

[tex]P(Z\leq a)=P_{4}=0.04[/tex]

[tex]\Rightarrow \Phi(a)=0.04[/tex]

[tex]\Rightarrow a=\Phi^{-1}(0.04)[/tex]

[tex]\Rightarrow \mathbf{a\approx -1.75} [ excel function : =NORMSINV(0.04) ][/tex]

the z score that corresponds to P4 is = -1.75

A Z-table, also referred to as a standard normal table, is an essential reference tool in statistical analysis. Its primary functions include calculating areas and probabilities under the standard normal distribution curve based on given values of z-scores.

In most cases, it provides cumulative probabilities for z- scores between -3.49 and 3.49, approximated to two decimal places.

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a). The formula for g, which determines x's half, is g(x) = 1/2 x

b). f(x) = x + 2

c). (fog)(x) = 1/2 x + 2

d). (fog) (52) = 28

The relationship between two sets of data, known as the input and output, is described mathematically by a concept known as a function.

An operation is applied to an input value by a function, which then produces an output value that matches the input value.

a). The formula for g, which determines x's half, is g(x) = 1/2 x

b). The formula for adding 2 to x is: f(x) = x + 2

c). Plugging g(x) into f(x) yields the function (fog)(x), which is as follows:

(fog)(x) = f(g(x))

f(1/2 x) = 1/2 x + 2

d). We must evaluate (fog)(52) to obtain the sale price of a shirt with an original cost of $52 as follows:

= (fog) (52) = 1/2(52) + 2

= 26 + 2

= 28

Thus, the shirt's ultimate retail price is $28.

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The total number of beds in Shelter B is 10.2. This is because the ratio of the occupancy of Shelter A to Shelter B is 14:25, meaning that if Shelter A is 70% occupied, then Shelter B must be 50% occupied.

Occupancy is used to measure the efficiency of a business or facility by determining how often a space is used, how long people stay in the space, and whether or not the space is being used to its full potential.

To calculate the number of beds in Shelter B, we need to first calculate the total number of beds in Shelter A. Since Shelter A is 70% occupied, we can use the following equation to calculate the total number of beds in Shelter A:

Total beds in Shelter A = (Occupied beds in Shelter A ÷ 70%) x 100%

Total beds in Shelter A = (400 ÷ 70%) x 100%

Total beds in Shelter A = 571.43

Since the ratio of the occupancy of Shelter A to Shelter B is 14:25, we can use the following equation to calculate the total number of beds in Shelter B:

Total beds in Shelter B = (Total beds in Shelter A x 25%) ÷ 14

Total beds in Shelter B = (571.43 x 25%) ÷ 14

Total beds in Shelter B = 10.2

Therefore, the total number of beds in Shelter B is 10.2. This is because the ratio of the occupancy of Shelter A to Shelter B is 14:25, meaning that if Shelter A is 70% occupied, then Shelter B must be 50% occupied. As a result, the total number of beds in Shelter B is 10.2.

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The total distance covered by Jeremy is 1320 m

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

For sapling 1 = No distance is covered.

For sapling 2, distance covered = 10 m

Return distance=10 m

For sapling 3, distance covered =20 m

Return distance=20 m and so on

Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...

Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12

Total distance covered = 122 [2(0) + (12 − 1) 20 ]

Total distance covered = 6 (11)(20) = 1320 m

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Complete question:

There are 12 saplings to be planted in a straight line at an interval of 10 m between

two consecutive saplings. Jeremy can carry only one sapling at a time and he has to

come back to the original point to take the next sapling. He plants 12 saplings in this

manner, planting the first sapling at the original point. After planting all the saplings,

he comes back at the original point,

In the process, what is the total distance that Jeremy covers?

​

On average, it will take us two to three inquiries to discover a kid who enjoys a salad for lunch.

The idea of probability is used to determine the likelihood or probability that a given occurrence will take place.

It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that it is guaranteed to happen.

Probabilities can be expressed using percentages, decimals, or fractions.

The likelihood that any particular student will choose a salad is 20%, or 0.2, assuming that each student's taste for lunch is independent of the preferences of the others.

There is a 0.2 chance that the first student you question will say they prefer a salad. You go on to the next kid if they don't want a salad.

Given that the first student didn't like a salad, there is a 0.2 chance that the second student will as well. None of the first two pupils had a (1-0.2) (1-0.2) = 0.64 chance of preferring a salad.

Given that none of the n-1 students before them did, the likelihood that the nth student would prefer a salad is similarly 0.2. (1-0.2)n-1 is the likelihood that none of the first n-1 students will choose a salad.

In order to identify a student who prefers a salad, you must thus question an anticipated number of students: E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...

Although this is an infinite series, by truncating it after a predetermined number of words, we may approximate it. Say we decide to quit after ten terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48

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We have expressed the expression 3 sec(-x) + 2 as a single fraction (3 + 2cos(x))/cos(x).

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. Expressions can be formed by combining variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

To write the expression 3 sec(-x) + 2 as a single fraction, we need to use some trigonometric identities and algebraic manipulation. Here are the steps:

Step 1: Recall that secant is the reciprocal of cosine, so we can rewrite the expression as:

3 (1/cos(-x)) + 2

Step 2: Cosine is an even function, which means that cos(-x) = cos(x). Therefore, we can simplify the expression to:

3 (1/cos(x)) + 2

Step 3: Recall that multiplying by the reciprocal is the same as dividing, so we can rewrite the expression as:

3/cos(x) + 2

Step 4: To add these fractions, we need a common denominator. The denominator of the first fraction is cos(x), and the denominator of the second fraction is 1. To get a common denominator, we can multiply the second fraction by cos(x)/cos(x):

3/cos(x) + 2(cos(x)/cos(x))

Simplifying the second term:

3/cos(x) + 2cos(x)/cos(x)

Step 5: Combining the fractions, we have:

(3 + 2cos(x))/cos(x)

Therefore, we have expressed the expression 3 sec(-x) + 2 as a single fraction (3 + 2cos(x))/cos(x).

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Answer:

68°

Step-by-step explanation:

Total angle in a quadrant = 90°

x + 22° = 90°

x = 90 - 22

x = 68°

The percentage increase in the number of archers is 77%.

A value's percentage growth is a way to represent how much it has grown in comparison to its starting point. It is calculated by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values.

The following formula is used to determine the percentage increase:

(New Value - Original Value) / Original Value * 100 is the formula for percentage increase.

The percentage increase is given by the formula:

Percentage Increase = (New Value - Original Value) / Original Value * 100

Now, given that there were 1158 more archers in 2012 and 2013 and from the table we have the archers in 2012-13 = 2645 the archers in 2011-12 is:

2645- 1158 = 1487

Thus,

percentage increase = 1158/ 1487 (100) = 77%

Hence, the percentage increase in the number of archers is 77%.

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As a result, the total number of pupils i Ms. Morales' class is 10x = 10(3) = 30.

30 pupils is the right response.

In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers.

If the boy-to-girl ratio in Ms. Morales' class is 3:7, the class may be divided into 10 equal portions, with three males and seven girls.

If x equals the number of guys in the class, then the number of girls in the class is 7x.

The total number of pupils in the class is the sum of the male and female students:

Total number of pupils = 3 times + 7 times = 10 times

To get the value of x, we must first determine the total number of pupils in the class. Ms. Morales's school has class sizes ranging from 22 to 34 pupils each class. Because 10x is the total number of pupils in the class, we must find an x value that gives us a total number of students between 22 and 34.

Let's see whether x = 2 works. If x equals 2, the total number of pupils in the class is 10x = 20, which is insufficient.

Let's see whether x = 3 works. If x = 3, the total number of pupils in the class is 10x = 30, which is between 22 and 34.

As a result, the total number of pupils in Ms. Morales' class is 10x = 10(3) = 30.

30 pupils is the right response.

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The total number of students in Ms. Morales's class is 84.

None of the given options is correct. The correct answer is 84.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other.

Let's first assume that the total number of students in Ms. Morales's class is x.

According to the problem statement, the ratio of boys to girls is 3:7. This means that out of every 3 + 7 = 10 students, 3 are boys and 7 are girls. Therefore, we can write:

Number of boys = (3/10)*x

Number of girls = (7/10)*x

The problem statement also tells us that the class sizes range from 22 to 34 students. This means that the total number of students x must be a multiple of both 3 and 7, and it must also be between 22 and 34 inclusive.

To find the possible values of x, we can list the multiples of 3 and 7 that are between 22 and 34:

Multiples of 3: 24, 27, 30, 33

Multiples of 7: 28

We can see that the only multiple of both 3 and 7 that is between 22 and 34 is 21*4 = 84. Therefore, the total number of students in Ms. Morales's class is 84.

Answer: None of the given options is correct. The correct answer is 84.

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If a person does 1.5 hours of bicycling per day for 5 days a week, they would burn approximately 3,750 calories in a week.

A person's age, gender, height, weight, and level of activity determine the average number of calories they need to consume each day to meet their energy needs and maintain their weight.

Individual factors such as age, gender, weight, height, and level of activity influence the average calorie intake.

If an average person burns 250 calories per half-hour while bicycling, then they would burn 500 calories per hour of bicycling.

So, if a person does 1.5 hours of bicycling per day, they would burn 1.5 x 500 = 750 calories per day.

If they work out 5 days a week, then the total number of calories burn in a week would be:

750 calories/day x 5 days/week = 3,750 calories/week

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After solving the equation we know that the mass of Sean and Ian is 62kf and 59.5 ks respectively.

Equation: A statement stating the equality of two expressions containing variables or numerical values.

Equation: A formula that uses the equals sign to combine two expressions and declare their equality.

In essence, equations are questions, and the methodical pursuit of solutions to these questions has served as the driving force behind the creation of mathematics.

Sean mass = x

Lan mass = x - 2.5

Then, form the equation and solve it as follows:

x + (x - 2.5) = 121.5

x + x - 2.5 = 121.5

2x - 2.5 = 121.5

2x = 121.5 + 2.5

2x = 124

x = 124/2

x = 62

Then, x - 2.5 = 59.5.

Therefore, after solving the equation we know that the mass of Sean and Ian is 62kf and 59.5 ks respectively.

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Answer:

A=40.8 B=8

Step-by-step explanation:

A Explanation

£7.20*3=£21.6

£9.60*2=£19.2

19.2+21.6=40.8

B Explanation

£9.60*3=£28.8

86.40-28.8=57.6

57.6/7.20=8

Answer:

57° + 124° + 140° = 321°

360° - 321° = 39° (measure of missing interior angle)

39° + c = 180°, so c = 141°.

Answer:

c=141

Step-by-step explanation:

140+57+124=321

360-321=39

180-39=141

Applying the intersecting secants theorem, the length of segment KL is approximately, 45.8.

According to the intersecting secants theorem, if two lines from a point outside a circle intersect the circle, then the product of the length of one line segment and its portion outside the circle is equal to the product of the length of the other line segment and its portion outside the circle.

Using the theorem, we have:

MN * MO = ML * MK

Substitute:

21 * 48 = 22 * KL

1,008 = 22KL

1,008/22 = KL

KL = 45.8 (nearest tenth)

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Answer: AC = 4.50

Step-by-step explanation:

sin 40 = x/7

x = sin 40 (7)

x = 4.50

Step-by-step explanation:

there are many possibilities, 4 of them really easy.

the endpoint of a diameter is simply a point on the circle arc.

the easy options are to assume that the center of the circle is on the x- or the y-axis.

let's go with the x-axis (we only need 2 circles : one with the center left, and one with the center right of the origin).

we know the radius is 3.

so, the center of either circle is 3 units away from the origin.

so, center of circle1 = (-3, 0), center of circle2 = (3, 0).

the equation for a circle is

(x - h)² + (y - k)² = r²

r is the radius, (h, k) is the center point.

equation for circle1 :

(x - -3)² + (y - 0)² = 3²

(x + 3)² + y² = 9

equation for circle2 :

(x - 3)² + (y - 0)² = 3²

(x - 3)² + y² = 9

you see ?

the other 2 easy options would be to put the centers on the y-axis : (0, -3) and (0, 3)

Answer:

[tex]y =\frac{x}{4}[/tex]

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with [tex]y=\frac{3}{x} -7[/tex], we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = [tex]x^\frac{1}{2}[/tex], even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with [tex]y = \frac{x}{4}[/tex]. x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that [tex]y=\frac{x}{4}[/tex] is linear.

a) The 90% confidence interval for the proportion of adults that have blue eyes is given as follows: (0.087, 0.133).

b) As the interval does not contain 0.08, the belief that 8% of people have blue eyes is misguided.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 9%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The parameters for this problem are given as follows:

[tex]n = 500, \pi = \frac{55}{500} = 0.11[/tex]

The lower bound of the interval is given as follows:

0.11 - 1.645 x sqrt(0.11 x 0.89/500) = 0.087.

The upper bound of the interval is given as follows:

0.11 + 1.645 x sqrt(0.11 x 0.89/500) = 0.133.

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Answer:

To perform these operations, we need to ensure that the dimensions of the matrices match. Since k is a row matrix with 1 row and 4 columns, and L is a column matrix with 4 rows and 1 column, we need to transpose one of them to match the dimensions. Let's transpose k to get a column matrix with 4 rows and 1 column:

k^T = 2

3

4

3

Now we can perform the matrix operations:

1. k + L:

2 + 7 = 9 3 + 10 = 13 4 + 5 = 9 3 + 11 = 14

9 + 1 = 10 13 + 6 = 19 5 + 9 = 14 11 + 4 = 15

10 + 11 = 21 4 + 7 = 11 7 + 10 = 17 3 + 7 = 10

= 9 13 9 14

10 19 14 15

21 11 17 10

2. K - L:

2 - 7 = -5 3 - 10 = -7 4 - 5 = -1 3 - 11 = -8

9 - 1 = 8 13 - 6 = 7 5 - 9 = -4 11 - 4 = 7

10 - 11 = -1 4 - 7 = -3 7 - 10 = -3 3 - 7 = -4

= -5 -7 -1 -8

8 7 -4 7

-1 -3 -3 -4

3. 2k + 3L:

2(2) + 3(7) = 20 2(3) + 3(10) = 36 2(4) + 3(5) = 22 2(3) + 3(11) = 37

2(9) + 3(1) = 21 2(13) + 3(6) = 44 2(5) + 3(9) = 23 2(11) + 3(4) = 29

2(10) + 3(11) = 42 2(4) + 3(7) = 29 2(7) + 3(10) = 34 2(3) + 3(7) = 23

= 20 36 22 37

21 44 23 29

42 29 34 23

4. 3L - 2K:

3(7) - 2(2) = 17 3(10) - 2(3) = 27 3(5) - 2(4) = 7 3(11) - 2(3) = 29

3(1) - 2(9) = -15 3(6) - 2(13) = -11 3(9) - 2(5) = 17 3(4) - 2(11) = -14

3(11) - 2(10) = 13 3(7) - 2(4) = 14 3(10) - 2(7) = 16 3(7) - 2(3) = 15

= 17 27 7 29

-15 -11 17 -14

13 14 16 15