Use the limit definition of the derivative to find a formula for f'(x) given f(x) = 3x^2 − 5

B. Use your result from part a to evaluate f'(− 1).

Answer:

Let's break down the given sentence into an equation.

Let's assume the number is represented by 'x'.

The product of two and a number: 2x

Eight less than the product of two and a number: 2x - 8

Equals four: 2x - 8 = 4

Therefore, the equation is 2x - 8 = 4.

Answer: 173 centimeters of ribbon left

Step-by-step explanation:

Antonio starts with 2 meters of ribbon, which is equal to 200 centimeters (since 1 meter = 100 centimeters). He cuts off 27 centimeters to decorate the gift, so he is left with:

200 - 27 = 173 centimeters

Therefore, Antonio has 173 centimeters of ribbon left.

The linear regression equation for the data given in the table is presented as follows:

y = 0.51x + 1.07.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.

The points for the data-set in this problem are given as follows:

(4,2), (6, 5), (12, 8), (17,9).

Inserting these four points into a linear regression calculator, the linear regression equation for the data given in the table is presented as follows:

y = 0.51x + 1.07.

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Answer:

Let's assume Adrian worked for x hours. Then, Bryan worked for (x + 8) hours.

According to the problem, the total hours worked by both is 88, so we can set up the equation:

x + (x + 8) = 88

Simplifying the equation:

2x + 8 = 88

Subtracting 8 from both sides:

2x = 80

Dividing both sides by 2:

x = 40

So Adrian worked for 40 hours and Bryan worked for 48 hours (since Bryan worked 8 hours more than Adrian).

Answer:

Adrian: 40 hours

Bryan: 48 hours

Step-by-step explanation:

Answer:

4 units

Step-by-step explanation:

Since the x-value is the same in both ordered pairs, you can just figure out the y-step ([tex]y_{2} -y_{1}[/tex]) and get your distance. -10 - (-6) = -4, so a distance of 4 units (negative sign does not matter in this case).

If both the x-values and y-values were different, another way to solve is to figure out the y- and x-steps and plug them into the Pythagoras theorem [tex]A^2+B^2 = C^2[/tex], with A being the horizontal distance (x-step) and B being the vertical distance (y-step).

You can also find the distance between 2 points by using the distance formula, which is  [tex]d = \sqrt{(x_{2}-x_{1})^{2} - (y_{2}-y_{1})^{2}[/tex]. After inserting the x- and y-coordinates of your ordered pair you get  [tex]d = \sqrt{(3-3)^{2} - (-10-(-6))^{2}[/tex]
Simplifying:
[tex]d = \sqrt{- (-10-(-6))^{2}}[/tex].  [tex](3-3)^{2}[/tex] was eliminated.
Then we distribute the negative signs: [tex]d = \sqrt{- (-10+6)^{2}}[/tex] --> [tex]d = \sqrt{(10-6)^{2}}[/tex].
[tex]d = \sqrt{(4)^{2}}[/tex] --> [tex]d = \sqrt{16}[/tex] --> [tex]d = 4[/tex]
So, the distance between the points is 4 units.
Side note: The distance formula works in the same way as the Pythagoras theorem.

The value of cos(2x+y) is -12/65.

Cosine, commonly denoted as cos, is a mathematical function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In other words, it is the ratio of the length of the adjacent side of an angle to the hypotenuse of the right triangle containing that angle. Cosine is one of the basic trigonometric functions, along with sine and tangent, and is widely used in mathematics, physics, and engineering to model various phenomena.

Cosine is periodic with a period of 2π, and its values range from -1 to 1. When the angle is 0°, the cosine is equal to 1, indicating that the adjacent side of the triangle is equal to the hypotenuse.

We can use the trigonometric identities for cosine to find cos(2x+y), using the values of x and y given:

cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)

To find cos(2x), we can use the double angle identity for cosine:

cos(2x) = cos²(x) - sin²(x)

To find cos(x) and sin(x), we can use the fact that x = sin⁻¹(4/5) and the Pythagorean theorem:

sin(x) = 4/5

cos(x) = √(1 - sin²(x)) = √(1 - 16/25) = 3/5

Substituting these values into the double angle identity, we get:

cos(2x) = cos²(x) - sin²(x) = (3/5)² - (4/5)² = -7/25

To find sin(2x), we can use the double angle identity for sine:

sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5) = 24/25

To find cos(y) and sin(y), we can use the fact that y = tan⁻¹(12/5) and the Pythagorean theorem:

sin(y) = 12/13

cos(y) = 5/13

Substituting these values into the expression for cos(2x+y), we get:

cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)

= (-7/25)(5/13) - (24/25)(12/13)

= -60/325

= -12/65

Therefore, cos(2x+y) = -12/65.

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Answer:

So the answer is 24.2

Step-by-step explanation:

Good luck to you!

according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.

What is a linear equation?

Based on the given linear model, we know that Marie's best 200 meter time (y) is a function of the number of weeks of training (x), and can be calculated using the equation:

y = -0.4x + 29.8

To find Marie's lowest time after 14 weeks, we simply need to substitute x = 14 into the equation and solve for y:

y = -0.4(14) + 29.8

y = -5.6 + 29.8

y = 24.2

Therefore, according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.

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Answer: To find (g∘f)(x), we need to first find the composite function g(f(x)):

g(f(x)) = g(2x - 2)

We can now substitute the expression for f(x) into g(x):

g(f(x)) = g(2x - 2) = 6(2x - 2)^2 - 3

Expanding the squared term, we get:

g(f(x)) = 6(4x^2 - 8x + 4) - 3

Simplifying and combining like terms, we get:

g(f(x)) = 24x^2 - 48x + 21

Therefore, (g∘f)(x) = 24x^2 - 48x + 21.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the percentage of cars that were traveling east, we can use the following formula:

percentage = (part / whole) x 100%

where "part" is the number of cars traveling east, and "whole" is the total number of cars counted.

In this case, we know that 6,020 cars were traveling east, out of a total of 7,000 cars counted. So we can plug these values into the formula:

percentage = (6,020 / 7,000) x 100%

percentage = 0.86 x 100%

percentage = 86%

Therefore, 86% of the cars counted were traveling east across the toll bridge.

Therefore , the solution of the given problem of speed comes out to be it will take 4 hours to travel the same distance at an average speed of 90 km/h.

We can determine something's speed by keeping a watch on it from a distance. The amount of distance an object can move in a specific amount of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most popular pace measurements are miles per hour (mile), kilometres per hour (kilometres), and metres for each second (m/s) (mph).

Here,

Applying the algorithm

Distance is determined by multiplying time and motion.

We can make the two equations equal because we know that the distance travelled in both scenarios is the same:

Distance = time + speed1

1 = time2 + speed2

where time1 is the first time (3 hours), speed1 is the first average speed (120 km/h), speed2 is the second average speed (90 km/h), and we're trying to determine time2.

Inputting the numbers provided yields:

Distance: 360 km at 120 km/h for three hours.

We can now determine the time2:

360 kilometres are equal to 90 kilometres per hour multiplied by two.

time2 = 360 km x 90 km/hr = 4 hours

Therefore, it will take 4 hours to travel the same distance at an average speed of 90 km/h.

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Answer:

-3

Step-by-step explanation:

i hope thisis the right aswrr

Answer:

½(a+b)h

½(24+32)×18

504ft²

I might be wrong

Answer: To subtract mixed numbers with different denominators, we need to convert them into like fractions first.

14 1/3 can be converted to an improper fraction as follows:

14 1/3 = (14 x 3 + 1) / 3 = 43/3

6 5/8 can be converted to an improper fraction as follows:

6 5/8 = (6 x 8 + 5) / 8 = 53/8

Now we can subtract the fractions:

43/3 - 53/8

To get a common denominator, we can multiply the denominators together: 3 x 8 = 24

43/3 x 8/8 = 344/24

53/8 x 3/3 = 159/24

Now we can subtract the numerators:

344/24 - 159/24 = 185/24

Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 13/24 as a mixed number in simplest form.

Step-by-step explanation:

The simplified value of 14 1/3- 6 5/8 is 7 17/24.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

To subtract 6 5/8 from 14 1/3, we need to have the same denominator.

Converting the mixed numbers to improper fractions, we get:

14 1/3 = 43/3

6 5/8 = 53/8

Now, we need to find a common denominator, which is 24.

Multiplying the numerator and denominator of 43/3 by 8 and 53/8 by 3, we get:

43/3 * 8/8 = 344/24

53/8 * 3/3 = 159/24

Now, we can subtract:

43/3 - 53/8 = (344/24) - (159/24) = 185/24

Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 17/24 as a mixed number.

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The correct statements are:

A. The independent variable is the number of boxes of cinnamon rolls Claude buys.

B. The dependent variable is the amount of money Claude spends on the cinnamon rolls.

What is independent variable?

The independent variable is the variable that is manipulated or controlled by the experimenter, and in this case, Claude is choosing how many boxes of cinnamon rolls to buy.

1. The dependent variable is the variable that is affected by the independent variable, and in this case, the amount of money Claude spends depends on the number of boxes he buys.

Therefore, statement A and B are correct, while C, D, and E are not true in this context.

2. Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a similar sampling probability than others. (FALSE)

3. Ruben randomly called 100 phone numbers in his town in order to survey them about their shopping habits. 55 people decided to participate in the survey.

This is an unbiased sample. (FALSE)

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a) The 8 in the number 24.387 is in the hundredths place, its value is 8/100 or 2/25.

b) One and three quarter million can be written in figures as 1,750,000.

c) 2/10 or 1/5.

d) 0.26 < 0.62 < 2.06 < 6.2

e) 13.4 > 13.390.33 = 1/38 = 2³

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

a) The 8 in the number 24.387 is in the hundredths place.

Therefore, its value is 8/100 or 2/25.

b) One and three quarter million can be written in figures as 1,750,000.

c) The 2 in the number 48.52 is in the tenths place.

Therefore, its value is 2/10 or 1/5.

d) Ordering the numbers from smallest to largest:

0.26 < 0.62 < 2.06 < 6.2

e) Completing the statements using the symbols <, > or = :

13.4 > 13.390.33 = 1/38 = 2³

Hence, The answers to each question are:

a)  8/100 or 2/25.

b) 1,750,000.

c) 2/10 or 1/5.

d) 0.26 < 0.62 < 2.06 < 6.2

e) 13.4 > 13.390.33 = 1/38 = 2³

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The subtraction of 3045 and 2572 by the column method has the result given as follows:

473.

When we subtract two amounts by the column method, we subtract digit by digit separately, hence:

3045

-2572

5 > 2, hence:

5 - 2 = 3.

4 is less than 7, and 0 is also less than 5, hence we must borrow from the last column, where 2 - 2 will be of zero, hence:

Hence the result of the subtraction is given as follows:

3045 - 2572 = 473.

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The probability that this person also sailed is 1.

What is probability?

In mathematics, probability is a measure of the likelihood or chance that an event will occur. It is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Out of 50 people, 40 took part in walking and 18 took part in sailing. However, 3 people did neither activity, which means that 40 + 18 - 3 = 55 people took part in at least one of the activities.

Let's represent the set of people who walked as A, and the set of people who sailed as B. We want to find the probability that a randomly chosen person from A is also in B, which can be represented as P(B|A).

Using the formula for conditional probability, we have:

P(B|A) = P(A and B) / P(A)

We know that P(A and B), the probability that a person took part in both walking and sailing, is 50 - 3 = 47 (since 3 people did neither activity). We also know that P(A), the probability that a person took part in walking, is 40.

Therefore,

P(B|A) = 47 / 40

which simplifies to

P(B|A) = 1.175

probabilities cannot be greater than 1, so the actual probability is 1, meaning that it is certain that a person who walked also sailed.

Hence, The probability that this person also sailed is 1.

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Answer:

First, let's find the fraction of people wearing green or red shorts:

1/4 + 1/6 = 3/12 + 2/12 = 5/12

This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):

1 - 5/12 = 7/12

So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:

7/12 x 24 = 14

Therefore, 14 people are wearing blue shorts.

Step-by-step explanation:

Answer:

To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.

Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:

4 parts + 6 parts + B parts = 24

Simplifying this equation, we get:

10 + B = 24

Subtracting 10 from both sides, we get:

B = 14

Therefore, 14 people are wearing blue shorts.

To double-check our answer, we can add up the number of people in each category:

4 parts out of 24 = 6 people wearing green shorts

6 parts out of 24 = 4 people wearing red shorts

B parts out of 24 = 14 people wearing blue shorts

6 + 4 + 14 = 24, which matches the total number of people in the race.

Answer:

[tex]y = -\frac{3x}{4} + 3[/tex]

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Remember to do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 3x from both sides of the equation:

[tex]3x + 4y = 12\\4y + 3x (-3x) = 12 (-3x)\\4y = -3x + 12[/tex]

Next, divide 4 from both sides of the equation:

[tex]4y = -3x + 12\\\frac{(4y)}{4} = \frac{(-3x + 12)}{4} \\y = \frac{-3x + 12}{4}\\ y = -\frac{3x}{4} + 3[/tex]

[tex]y = -\frac{3x}{4} + 3[/tex] is your answer.

~

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The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.

What is Normal Distribution ?

A normal distribution is a continuous probability distribution that is often used in statistics to model a wide variety of phenomena, such as measurements of height, weight, or IQ.

The normal distribution is symmetric. This means that the distribution is mirror-image symmetric around its mean, so that the same proportion of values lie on either side of the mean.

The normal distribution is characterized by two parameters: its mean (μ) and standard deviation (σ). The mean is the center of the distribution, while the standard deviation measures the spread of the distribution.

The total area under the normal distribution curve is equal to 1. This means that the probability of any event occurring is between 0 and 1.

The empirical rule, also known as the 68-95-99.7 rule, applies to normal distributions. This rule states that approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean.

Therefore, The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.

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Answer:

BE=15

Step-by-step explanation:

Since E is the center, BE=2x+1

And AC is 6x-12 with E being a midpoint.

Since AC is 2 segments and BE is only 1 then you multiply 2x+1 by 2 so that

you can find x. You multiply 2x+12 by 2 because E is the midpoint so that means ED is the same value as BE

6x-12=4x+2

BD=AC

6x-4x-12=2

2x=2+12

2x=14

x=7

BE= 2x+1

2(7)=14+1=15

Answer:

yes

Step-by-step explanation:

It is a Pythagorean triangle 3-4-5

Hope this helps.

Answer: Here's a tree diagram that shows all the possible sequences of answers for four multiple-choice questions, each with five possible responses:

           /-- A -- A -- A -- A

          /

         /      /-- A -- A -- A -- B

        /      /-- A -- A -- B -- A

       /      /-- A -- B -- A -- A

      /      /-- B -- A -- A -- A

     /      /

    /      /         /-- A -- A -- B -- B

   /      /         /-- A -- B -- A -- B

  /      /         /-- A -- B -- B -- A

 /      /         /-- B -- A -- A -- B

/      /         /-- B -- A -- B -- A

/      /         /-- B -- B -- A -- A

      /

     /            /-- A -- B -- B -- B

    /            /-- B -- A -- B -- B

   /            /-- B -- B -- A -- B

  /            /-- B -- B -- B -- A

 /

/               /-- A -- B -- B -- B

/               /-- B -- A -- B -- B

               /-- B -- B -- A -- B

              /-- B -- B -- B -- A

Each branch in the tree represents the guess for one of the questions, and the letters A and B represent the possible answers. There are 5 branches coming out of each node in the tree because there are 5 possible answers for each question.

To find the probability of guessing the one sequence that contains all four correct answers, we multiply the probabilities of following the path A-A-A-A:

P(A-A-A-A) = (1/5) * (1/5) * (1/5) * (1/5) = 1/625

Therefore, the probability of guessing the one sequence that contains all four correct answers is 1/625 or about 0.16%.

Step-by-step explanation:

Step-by-step explanation:

you can simply solve this question by simple division

Answer:

1. 92 m²

2. 184 cm²

Step-by-step explanation:

1.

Look at the left triangle.

Imagine that the 8 m segment continues to the bottom, and you have a horizontal leg there.

The hypotenuse measures 15 m.

The vertical leg is 8 m + 4 m = 12 m.

a² + b² = c²

12² + b² = 225

b = 9

The horizontal leg is 12 m.

A = 2 × 12 m × 9 m / 2 - 4 m × 4 m

A = 92 m²

2.

Bottom rectangle: length = 20 cm; width = 7 cm

Upper trapezoid: bottom base = 20 cm - 13 cm = 7 cm; height = 15 cm - 7 cm = 8 cm; upper base = 4 cm

A = 20 cm × 7 cm + (1/2)(7 cm + 4 cm)(8 cm)

A = 184 cm²

Answer:

To find out what is the other 10%, you can use the following formula:

(100% - 90%) = 10%

So, if 144 is 90% of a value, we can divide 144 by 0.9 to find the total value:

144 / 0.9 = 160

Therefore, the other 10% of 160 is:

0.1 x 160 = 16

Step-by-step explanation:

Applying similar triangles the length of EB is 14.6

Similar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

DE and DF, EB and FC

The solution is worked out using sides BC and FE, then AC and DF

DE / EB = DF / FC

17.5 / EB = 13.1 / 10.9

cross multiplying

17.5 * 10.9 = 13.1 * EB

EB = 14.6

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