Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What is the output of the function f(x) = x + 21 if the input is 4? When the input is 4, the output of f(x) = x + 21 is .

Answer:

46 miles

Step-by-step explanation:

First, set up an equation:

(48 + 58 + 68 + 50 + x) ÷ 5 = 54

Add the miles in the parentheses:

(48 + 58 + 68 + 50 + x) ÷ 5 = 54

48 + 58 + 68 + 50 = 224

(224 + x) ÷ 5 = 54

Multiply by 5 on each side:

[(224 + x) ÷ 5] × 5 = (54) × 5

(224 + x) = 270

Subtract 224 on each side to isolate x:

(224 + x) - 224 = (270) - 224

x = 46 miles

Hope this helps! I'd appreciate brainliest but if not that's fine!

Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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Answer:

\(\left\begin{array}{ccccc}&0&0&0&0 \\ \times&&&&9 \\--&--&--&--&--\\& 0 & 0 & 0 & 0 \\--&--&--&--&-- \end{array}\right\)

Step-by-step explanation:

Now,

\(\left\begin{array}{ccccc}&M&A&T&H \\ \times&&&&9 \\--&--&--&--&--\\& H & T & A & M \\--&--&--&--&--\\ ^{a} & ^{b} & ^{c} & ^{d} \end{array}\right\)

where the small letters a,b, c and d refers to carried numbers.

Converting this to equations:

This equation comes from carrying remainders.

We know \(0 \le H \le 9\) because H is a single digit, so by the fourth equation,

9M+b=H

M=0 or 1 since any larger integer value of M will make H a double digit number.

If M=1, we have:

\(\left\begin{array}{ccccc}&1&A&T&H \\ \times&&&&9 \\--&--&--&--&--\\& H & T & A & 1 \\--&--&--&--&--\end{array}\right\)

The only multiple of 9 that will give a remainder of 1 is 9. Therefore:

In this case, H=9

However, even if A and T were to be 0, the least possible number

1009 X 9= 9081

Therefore:

M=0

And sure enough

\(\left\begin{array}{ccccc}&0&0&0&0 \\ \times&&&&9 \\--&--&--&--&--\\& 0 & 0 & 0 & 0 \\--&--&--&--&-- \end{array}\right\)

Answer:

its in there

Step-by-step explanation:

Answer: Solve the Inequality for h

Solve for h

Graph

Convert to Interval Notation

Evaluate

Write in y=mx+b Form

Find the Exact Value

Solve the Absolute Value Inequality for h

Convert to Set Notation

Plot

Write in Slope-Intercept Form

Solve the Rational Equation for h

Simplify

Add

Solve by Factoring

Describe the Transformation

Evaluate the Summation

Find the Absolute Max and Min over the Interval

Find the Product

Convert from Degrees to Radians

Convert to a Decimal

Subtract

Find the Slope

Find the Domain and Range

Find the Derivative - d/dh

Solve Using the Square Root Property

Find the Direction Angle of the Vector

Multiply

Find the Function Rule

Convert to a Simplified Fraction

Find the Area Between the Curves

Solve the Function Operation

Solve the System of Inequalities

Solve for h in Degrees

Find Where Increasing/Decreasing

Find the Maximum/Minimum Value

Write with Rational (Fractional) Exponents

Evaluate the Limit

Find the Slope and y-intercept

Solve by Isolating the Absolute Value for h

Find All Complex Solutions

Factor over the Complex Numbers

Find the Intersection

Find the Center and Radius

Convert to Radical Form

Find the Integral

Evaluate Using Summation Formulas

Evaluate Using Scientific Notation

Simplify/Condense

Determine if Linear

Graph Using a Table of Values

Reduce

Rationalize the Denominator

Find the Union

Find the Critical Points

Solve for h in Radians

Find the x and y Intercepts

Find the Inverse

Find the Perpendicular Line

Convert from Interval to Inequality

Solve by Completing the Square

Simplify the Matrix

Maximize the Equation given the Constraints

Convert to Regular Notation

Determine if the Relation is a Function

Write in Standard Form

Convert to Trigonometric Form

Split Using Partial Fraction Decomposition

Find the Zeros by Completing the Square

Find the Prime Factorization

Find the Local Maxima and Minima

Find the Quotient

Multiply the Matrices

Factor

Answer:  The acceleration is 0 after 4.5 seconds.

*The distance traveled in the last 15 seconds on the graph is about 225 meters.*

If the question means "distance traveled during the last 15 seconds before coming to a complete stop" The distance is 30 meters.

The attachment shows what I believe to be the missing right side of the graph showing the velocity at 0.

Step-by-step explanation: a.) at 4.5 seconds, the graph is momentarily flat; that is, the derivative, (the change in slope) is 0. There is no change in velocity at that point. Before that, the velocity is increasing, so there is positive acceleration. After that, the velocity is decreasing. So the acceleration is negative.

*The answer choices seem incorrect to me. for part b. Is there a typo?*

b.) From 10 seconds to 25 seconds, the "last 15 seconds" on the graph, the velocity is decreasing at a steady rate; the average velocity is 15m/sec

At  15m/sec × 15 sec, the distance traveled is 225 meters.

If we are to extrapolate to the point there the velocity is 0, assuming the steady rate of deceleration, the motorbike will reach that stopping point at 63.75 seconds. At 15 seconds before that, at 48.5 sec, it is traveling at 4m/sec.

The average velocity during the final 15 seconds is 2m/sec.

2m/sec × 15 sec = 30 meters.

I don't see that choice either, so I wonder if the question is missing something.

If someone else has a better explanation, I hope they they will answer and explain what I missed.

Answer:

I will only be answering B as A has already been correctly Anserd

B is 225

Step-by-step explanation:

You have to draw a trapezium on the graph and work out it's area so

17 + 13 = 30

30÷ 2 = 15

15 × 15 = 225

Answer:

a) Let's suppose that player 1 chooses rock, and the selection of player 2 can be thought as random.

If player 2 randomly selects rock, the result of the game is a draw.

if player 2 randomly selects papers, player 1 loses.

if player 2 randomly selects scissors, player 1 wins.

Then we have 3 options with the same probability, that will be:

1/3

This is, the probability of winning is equal to the quotient between the number of outcomes that make player one win (1, in this case, scissors) and the total number of outcomes (3) = 1/3

the probability of a draw is equal to the quotient between the number of outcomes that make a draw (1, in this case, rock) and the total number of outcomes (3) = 1/3

the probability of losing is equal to the quotient between the number of outcomes that make player one lose (1, in this case, paper) and the total number of outcomes (3) = 1/3

And remember that this will be the same for any selection of the player 1.

b) As we already found, the probability of winning for any selection is 1/3 = 0.333..

SOLUTION

solve for x



-5/3n = -3​

cross - multiply we have:

-5 = 3 n X 3

-5 = 9n

Divide both sides by 9, we have;

n = -5 / 9

(A−5)(A+4) I think that is the right answer

Answer:

-2

Step-by-step explanation:

Answer:

\(x=15\)°

Step-by-step explanation:

The sum of degree measures in a full angle (a circle) is (360) degrees. This means that the sum of all of the angles in this diagram is (360) degrees, as the angles form a full arc. Therefore, one can form an equation by adding up all of the angles and setting the equation equal to (360) degrees. Then one can substitute each angle value with the equation that is used to represent it, simplify, and use inverse operations to solve for the value of (x).

\((m<AMB)+(m<BMC)+(m<CMD)+(m<AMD)=(360)\)

Substitute,

\((46)+(4x-2)+(9x+6)+(8x-5)=360\)

Simplify,

\((46)+(4x-2)+(9x+6)+(8x-5)=360\)

\(21x+45=360\)

Inverse operations,

\(21x+45=360\)

\(21x=315\)

\(x=15\)

a) Find the dean’s eye view average class size and the student’s eye view average class size:Given that there are 16 seminar courses, each having 10 students each.Number of students in seminar courses: 16 × 10 = 160There are 2 large lecture courses, each having 100 students each.

Number of students in large lecture courses: 2 × 100 = 200

Dean’s view average class size is the simple average of the class sizes:Let’s find the Dean’s view average class size. There are 18 courses in total.

This can be obtained by dividing the total number of students by the total number of classes.

Student’s view average class size = Total number of students/Total number of classes

= 360/18

= 20

Therefore, the dean’s eye view average class size is 46.67 (approximately) and the student’s eye view average class size is 20.

Now, we need to prove that D 2, then (k/(k + 1)) - (1/n) < 0.

Therefore, we have:

S - D< (c2 - c1)*[(k/(k + 1)) - (1/n)]< 0

Hence, S < D.Therefore, the dean’s eye view average class size will be strictly less than the student’s eye view average class size, unless all classes have exactly the same size.

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Probability calculation: To calculate the probability that the temperature of Lake Larson will be greater than 86 degrees, we need to use the concept of standard deviation and the normal distribution.

Since we know the average temperature is 58 degrees and the standard deviation is 5 degrees, we can use these values to find the z-score for the temperature of 86 degrees. The z-score formula is given by: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get: z = (86 - 58) / 5 = 5.6.Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of 5.6. The probability is extremely small, close to 0. In other words, the chance that the temperature of Lake Larson will be greater than 86 degrees is very unlikely.

The distribution of temperatures of Lake Larson can be represented by a normal distribution curve. The mean of 58 degrees represents the center of the curve, and the standard deviation of 5 degrees determines the spread or variability of the temperatures. When we calculate the probability that the temperature will be greater than 86 degrees, we find a very low probability. This indicates that temperatures significantly higher than the average are rare occurrences. The distribution curve shows that most of the temperatures cluster around the mean of 58 degrees, with fewer temperatures occurring as we move towards the extremes.

This information is valuable for understanding the temperature patterns and making predictions about the likelihood of extreme temperatures. It suggests that temperatures above 86 degrees are highly unlikely and that Lake Larson tends to have a relatively stable temperature range centered around 58 degrees.

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The diameter of the sphere is 1.2 meters.

We know that for a sphere of radius R, the surface area is given by the formula:

S = 4πR²

Where π = 3.14

Here we know that the surface area is 4.5216m²

Then we can replace that and find the radius:

4.5216m² = 4*3.14*R²

Solving for R:

R = √(4.5216m²/(4*3.14))

R = 0.6m

Then the diameter, two times the radius, is:

D = 2*0.6m

D = 1.2 meters.

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Answer:

18

Step-by-step explanation:

Round 6.1 down to 6. If you divide 18 by 3 you get 6.

Therefore, 6 is one third of 18.

Answer:

ygjjjyc

Step-by-step explanation:

trzerxcgvjyu

Answer:

Step-by-step explanation:

2kg/m² convert to g/100cm²

1 kg=1000 g

2kg=  ???

2*1000=2000kg

m      ⇒      100cm

m²     ⇒      10000 cm²

2kg/m²=2*1000/(10000/100) cm²

=2000/100 cm²

250*1000=250000

1 hectare=10000 m²

250000/10000 g/m²

Given:

The first four terms of a sequence are:

8, 5, 2, -1

To find:

The function that defines the given sequence.

Solution:

We have,

8, 5, 2, -1

The differences between two consecutive terms are:

\(5-8=-3\)

\(2-5=-3\)

\(-1-2=-3\)

The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.

The nth terms of an arithmetic sequence is:

\(f(n)=a+(n-1)d\), for \(n\geq 1\)

Where, a is the first term and d is the common difference.

Putting \(a=8,d=-3\), we get

\(f(n)=8+(n-1)(-3)\)

\(f(n)=8-3(n-1)\)

\(f(n)=-3(n-1)+8\), for \(n\geq 1\)

Therefore, the correct option is A.

The electrical potential at the point (0,2.2)m is -8.617 V

a) The electrical potential at the origin:

We know that the electric potential at any point P due to a point charge q at a distance r from it is given as:

V = kq/r

where k is a constant and its value is 9 × 10^9 Nm^2/C^2.q = 6 μC = 6 × 10^-6 C  

Distance between the charge and the origin, r1 = sqrt((-4.1)^2 + 0^2) = 4.1 m.

Distance between the charge and the point (0,2.2)m, r2 = sqrt((-4.1)^2 + (2.2)^2) = 4.6 m.

The electrical potential at the origin isV1 = kq/r1= 9 × 10^9 × 6 × 10^-6 / 4.1= 13.846 V

Thus, the electrical potential at the origin is 13.846 V.

b) The electrical potential at the point (0,2.2)m:

Let's find the potential at the point (0,2.2)m.

So the distance between q1 and the point (0,2.2)m is, r11 = sqrt((-4.1)^2 + (2.2)^2) = 4.6 m

Now, the distance between q2 and the point (0,2.2)m is,r22 = sqrt((-6)^2 + (2.2)^2) = 6.2804 m

So, the electrical potential at the point (0,2.2)m is given by,

V2 = kq1/r11 + kq2/r22

    = 9 × 10^9 × 6 × 10^-6 / 4.6 + 9 × 10^9 × -7 × 10^-6 / 6.2804= -8.617 V

Thus, the electrical potential at the point (0,2.2)m is -8.617 V.

The electrical potential at the origin is 13.846 V..

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To find the volume of the given solid using polar coordinates, we integrate the function over the appropriate range of values for the radial coordinate and the angle.

The given solid consists of a cone and a ring in the xy-plane. The cone is defined by the equation z = √(x² + y²), which represents a right circular cone with its vertex at the origin and opening upwards. The ring is defined by the inequality 1 ≤ x² + y² ≤ 64, which represents a circular region centered at the origin with an inner radius of 1 unit and an outer radius of 8 units.

To evaluate the volume using polar coordinates, we can express the equations in terms of the radial coordinate (r) and the angle (θ). In polar coordinates, the cone equation becomes z = r, and the ring equation becomes 1 ≤ r² ≤ 64. To set up the integral, we need to determine the range of values for r and θ. For the radial coordinate, r ranges from 1 to 8, as that corresponds to the region defined by the ring. For the angle θ, we can integrate from 0 to 2π, covering a full revolution around the origin.

The volume integral is then given by V = ∫∫∫ r dz dr dθ over the region defined by 1 ≤ r² ≤ 64 and 0 ≤ θ ≤ 2π. By evaluating this triple integral, we can find the volume of the solid.

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

The value of 'd' in the proportion 3:d:27:45 is 5

A proportion can simply be defined as a mathematical comparison of two different numbers.

The numbers mostly describes a comparison between people, elements, quantities, or things.

It is also seen as an equation having two ratios which are proportionally  set equal to each other.

The mathematical operations involved in proportion includes;

Given the expression:

3:d:27:45

This is represented as;

3 = d

27 = 45

To determine the value of 'd', we have;

cross multiply

27d = 135

Make 'd' the subject of formula by dividing both sides by 27

d = 135/27

d = 5

Hence, the value is 5

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The complete question:

3:d:27:45 . Find the value of d in the proportion

Answer:

Each cookbook cost $15.15.

Step-by-step explanation:

Since the statement indicates that four cookbooks and one novel cost $68.75, you can write the following equation:

4x+y=68.75, where:

x is the price of cookbooks

y is the price of novels

Also, given that the novel cost 7 dollars less than a cookbook, you can write the following equation:

x=y+7

Now, you can replace x=y+7 in the first equation:

4(y+7)+y=68.75

4y+28+y=68.75

5y=40.75

y=40.75/5

y=8.15

Now, you can replace the value of y in x=y+7:

x=8.15+7

x=15.15

According to this, the answer is that each cookbook cost $15.15.

Answer:

ok i dont knkw what is that lol

When performing calculations, retain 9 decimal places throughout the calculations. However, when reporting the final answers, round them to 2 decimal places. This applies to various units such as years, dollars, percentages, and times. For example, if the answer is 9 times, report it as 9.00, and if the answer is $48,000, report it as 48,000.00. Be precise with rounding and reporting to maintain consistency and accuracy.

In financial calculations, it is important to maintain precision during intermediate calculations to minimize rounding errors. By retaining 9 decimal places throughout the calculations, we can ensure that the accuracy is preserved. However, when presenting the final results, it is common practice to round the numbers to a more readable format with 2 decimal places.

For instance, in Problem 1, calculating the current bond price involves complex calculations using the bond's coupon rate, years to maturity, and yield to maturity (YTM). Throughout the calculation, it is necessary to maintain the accuracy of intermediate values with 9 decimal places. However, when reporting the final bond price, we round it to 2 decimal places for clarity.

Rounding to 2 decimal places is also applied in other problems, such as calculating bond yields (Problem 2 and Problem 4), coupon rates (Problem 3), real rates of return (Problem 5 and Problem 6), and stock values (Problem 7, Problem 8, Problem 9, and Problem 10). By following the rounding guidelines, we ensure consistent and precise reporting of the results.

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Answer:

-1.2

Step-by-step explanation:

3n + 5 = 1/2(11n + 16)

3n + 5 = 5.5n + 8

5 = 2.5n + 8

-3 = 2.5n

-3/2.5 = n

-1.2 = n

Hope this helps!

Answer:

\(n=-1.2\)

Step-by-step explanation:

First, solve both sides of the equation:

\(3n+5=\frac{1}{2} (11n+16)\)

\(3n+5=(\frac{1}{2} )(11n)+(\frac{1}{2} )(16)\) (Distribute)

\(3n+5=\frac{11}{2} n+8\)

Then, subtract 11/2 n from both sides:

\(3n+5-\frac{11}{2}n=\frac{11}{2} n+8-\frac{11}{2} n\)

\(\frac{-5}{2}n+5=8\)

Now, subtract 5 from both the sides:

\(\frac{-5}{2} +5-5=8-5\)

\(\frac{-5}{2} n=3\)

For the last step, multiply both the sides by 2 / -5

\((\frac{2}{-5} )*(\frac{-5}{2} )=(\frac{2}{-5} )*(3)\)

\(n=\frac{-6}{5}\)

Convert it to decimal:

\(n=-1.2\)

With n = 1, the total time elapsed before the ball comes to rest is 0.4 units of time. The total time elapsed before the ball comes to rest is represented by the formula t = (1/2)∑(0.8)^n as n approaches infinity.

The ball takes the same amount of time to bounce up as it does to fall, starting from the second bounce (n = 1). This means that for each subsequent bounce, the time it takes for the ball to reach its maximum height and return to the ground is the same.

The total time elapsed before the ball comes to rest is given by the formula t = (1/2)∑(0.8)^n, where n represents the number of bounces and ∑ denotes the summation notation. In this case, the summation starts from n = 1 and goes to infinity.

To calculate the total time, we substitute n = 1 into the formula: t = (1/2)(0.8)^1 = 0.4. Therefore, with n = 1, the total time elapsed before the ball comes to rest is 0.4 units of time.

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In the question, the independence assumption may have been violated, while the Nearly Normal Condition is likely justified. Therefore, the use of the Student-t model for inference may be unreliable.

a) In order to perform a hypothesis test on the claim made by the diet guide, we need to assess the assumptions and conditions required for reliable inference. The independence assumption states that the observations are independent of each other. In this case, it is not explicitly mentioned whether the yogurt samples were independent or not. If the samples were obtained from the same batch or were not randomly selected, the independence assumption could be violated.

Regarding the Nearly Normal Condition, which assumes that the population of interest follows a nearly normal distribution, it is reasonable to assume that the distribution of calorie counts in vanilla yogurt is approximately normal. However, since we do not have information about the population distribution, we cannot definitively justify this condition.

b) The appropriate hypotheses for testing the claim made by the diet guide would be:

H0: The average calories per serving of vanilla yogurt is 120.

HA: The average calories per serving of vanilla yogurt is not equal to 120.

To test these hypotheses, we can use a t-test for a single sample. The test statistic (t) can be calculated by taking the mean of the sample calorie counts and subtracting the claimed average (120), divided by the standard deviation of the sample mean. The p-value can then be determined using the t-distribution and the degrees of freedom associated with the sample.

Without the actual sample mean and standard deviation, it is not possible to provide the specific test statistic and p-value for this scenario. These values need to be calculated using the given data (calorie counts) in order to draw a conclusion about the claim made by the diet guide.

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A regular linear regression model is statistically helpful in providing a good fit to the information that can be used to make precise predictions about new information agendas.

A linear regression model is useful when the explanation of a significant amount of variation of the dependent variable utilizes one or more independent variables. The usability of a linear regression model can be comprehended by examining various statistical measures for instance

R-squared value of 1 shows that all of the changes in the dependent variable are elaborated by the independent variable, Hence, an R-squared value of 0 points that none of the variations is elaborated

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