Need this for a math lesson

Check the picture below.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}[/tex]

Answer:

-2

[tex]\hrulefill[/tex]

Step-by-step explanation:

The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

The given interval is -4 ≤ x ≤ -3, so:

From observation of the given graph, the values of f(a) and f(b) are:

[tex]f(a)=f(-4)=-4[/tex]

[tex]f(b)=f(-3)=-6[/tex]

Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:

[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}[/tex]

Therefore, the average rate of change of the function f(x) on the given interval is -2.

Answer:

60

Step-by-step explanation:

3.92 = (6.56/100) * _

To solve for _, we can multiply both sides by 100:

100 * 3.92 = (6.56/100) * _

100 * 3.92 = 6.56 * _

_ = (100 * 3.92) / 6.56

Therefore, _ = 60.

Answer: 60

Step-by-step explanation:

The probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778.

To calculate the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice, we need to find the number of ways the dice can be rolled to get a sum less than or equal to 6 and divide it by the total number of possible outcomes.

There are 6 x 6 = 36 possible outcomes when rolling a pair of dice, since there are 6 possible outcomes for each die. To get a sum less than or equal to 6, the only possible outcomes are:

1+1 = 2

1+2 = 3

1+3 = 4

1+4 = 5

2+1 = 3

2+2 = 4

2+3 = 5

3+1 = 4

3+2 = 5

4+1 = 5

There are 10 possible outcomes that result in a sum less than or equal to 6. Therefore, the probability of rolling a sum less than or equal to 6 is:

P(sum less than or equal to 6) = number of favorable outcomes / total number of possible outcomes

P(sum less than or equal to 6) = 10 / 36

Simplifying this fraction, we get:

P(sum less than or equal to 6) = 5 / 18

Therefore, the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778 when rounded to four decimal places.

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Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

rate X time = distance

rate  = distance / time    <=====we want minimum of this so make denominator as large as possible and numerator as small as possible

      distance = 595  KM    ( rounds up to 600 km)

        time = 8 hr 44 min  rounds down to 8 :40    you could make it 8:44.99)

595 km / (8 + 44.99/60) hr  = 68 km/hr

The dimension of rectangular piece of land is 17 x 12 square units in size.

The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.

The space occupied by a flat shape or an object's surface can be referred to as the area.

What is the rectangular area formula?

Rectangle area equals length x width

Let the rectangle plot's length and breadth be x and y, respectively.

Juliet has a 58-meter fence.

The rectangular piece of land's perimeter is 58 meters.

2(length + width) = 58

x + y = 58\2

⇒ x + y = 29

Moreover, the plot's total area is 204 square units.

x × y = 204

⇒ x × (29 - x) = 204

[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]

(x-12) (x-17) = 0

x = 12, x = 17

When, x= 17

y = 29 - 17 = 12m

when x = 12

y = 29 - 12 = 17m

As a result, the rectangular land parcel has dimensions of 17 x 12 square units.

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To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.

This conversion factor takes into account the difference in volume between a liter and a fluid ounce.

1 fl oz = 29.5735 mL

1 L = 1000 mL

So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:

(mg/L) * 1000 / 29.5735 = (µg/fl oz)

Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:

x (µg/fl oz) = x (mg/L) * 1000 / 29.5735

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The lower quartile is 2, the median is 5 and the upper quartile is 8.

What are quartiles?

The values that divide a list of numerical data into three quarters are known as quartiles.

We are given a data set as 1, 2, 3, 5, 5, 8, 8

From this, we get the median as 5 as median is the middle number of the data set.

We know that lower quartile is the median of the lower half of the data.

So, lower quartile is 2.

Upper quartile is the median of the upper half of the data.

So, upper quartile is 8.

Hence, the lower quartile is 2, the median is 5 and the upper quartile is 8.

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The completed statements with regards to the projectile motion of the football are presented as follows;

This graph is a nonlinear function

The hang time of the football is 3 seconds

The football reaches its maximum height when t = 1.5 seconds

The maximum height is about 11 meters

For t between t = 0 and t = 1.5, the height is increasing

The motion of a projectile is one that involves an object thrown into the air or into space, which is acted upon by only gravitational force.

The graph in the question, showing the scale on the x-axis obtained from a similar question on the internet, indicates that we get;

The x-intercept of the graph are; (0, 0), and (3, 0)

Therefore;

The time the football is in the air, which is the hang time of the football can be obtained from the difference between the x-values of the x-intercept as follows;

Hang time = 3 - 0 = 3

The graph indicates that the coordinates of the maximum height is (1.5, 11). Therefore;

The height at t = 0 is 0 meters, and the height at t = 1.5 seconds is 11 meters, therefore; the height is increasing between t = 0 and t = 1.5 seconds

For t between t = 0 and t = 1.5, the height is increasing

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Answer:

Nonlinear

3

1.5

11

increasing

Step-by-step explanation:

By knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.

The five number summary is a way to summarize the distribution of a set of data by providing information about its minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum. Using this summary, we can infer information about the location of specific percentiles.

For the 20th percentile, we can conclude that it lies between the minimum and the first quartile. The 20th percentile represents the value below which 20% of the data falls, so it must be less than or equal to the first quartile, which is the value below which 25% of the data falls. It must also be greater than or equal to the minimum.

For the 90th percentile, we can conclude that it lies between the third quartile and the maximum. The 90th percentile represents the value below which 90% of the data falls, so it must be less than or equal to the maximum, which is the largest value in the data set. It must also be greater than or equal to the third quartile, which is the value below which 75% of the data falls.

In conclusion, by knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.

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Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.

Therefore,

Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.. In this instance, the likelihood of Q and R is equal to P(Q) × P(R), which is 0.1804. The solution to this issue is this.

The complete question is:

Suppose Q and R are independent events. Find the probability of Q and R when P(Q)=0.41 Ans P(R)=0.44.

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The length of the hypotenuse BC in right  angled triangle ABC is 3.605 units.

A triangle is said to be right angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. Consequently, other names for this triangle include the right triangle and 90-degree triangle.

In right angle triangle if 90 degree angle is A then

[tex]AB^{2} +AC^{2} = BC^{2}[/tex]

And here length of altitude AB equals to 3 units and length of base  AC equals to 2 units And here length of hypotenuse BC equals to [tex]\sqrt{13}[/tex] units

[tex]AB^{2} +AC^{2} = BC^{2}[/tex]

[tex]3^{2} +2^{2} = \sqrt{13}[/tex]

[tex]\sqrt{13}[/tex]= 3.60555 unit

And here ans [tex]\sqrt{13}[/tex] is already give what we have to do just calculate the value of [tex]\sqrt{13}[/tex] which is = 3.605

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Answer:

To find a slope intercept in a table look what x is like this. ( 2,9) 2 is the x-intercept and 9 is the y-intercept. Furthermore, if you get a slope like 0,0 which is the origin put a dot on there.

Answer:

Step-by-step explanation:

use this equation

(y1-y2)/(x1-x2)

The equation of a line is y = -1/3x - 4

The general formula for the equation of a line is expressed as;

y = mx + c

Given that the parameters are;

From the information given, we have that;

Slope, m = -1/3

Substitute the values

-1 = -1/3(-9) + c

expand the bracket

-1 = 3 + c

collect like terms

= -4

Hence, the equation is y = -1/3x - 4

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The chance of seeing an advertisement on the front page if the newspaper is JKL is 86.3%.

Probabilities:

In science, the probability of an event is a number representing the probability that an event will occur. It is expressed as a number ranging from 0 to 1, or as a number ranging from 0% to 100% using percentage display. The more likely an event is to happen, the more likely it is to happen. The probability of an impossible event is zero. The probability of an event that must happen is 1. The probabilities of two complementary events A and B (A or B) add up to 1.

A simple example is a fair (unbiased) coin toss. When the coin is fair, the two possible outcomes (heads and tails) are equally likely. Since the two outcomes are complementary and the probability of heads is equal to the probability of tails, the probability of each of the two outcomes is 1/2.

Therefore,

After looking at the table, the percentage that represents JKL and a front page advertisement is 86.3%.

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(a) The number of possible schedules that the student can create from the offerings is 96.

(b) the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed is 48.

(c) the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the English 105 sections are closed is 4.

(a) To find the total number of possible schedules, we need to multiply the number of choices for each class:

Number of schedules = 4 x 2 x 3 x 4 = 96

So, there are 96 possible schedules that the student can create from the offerings.

(b) If two of the math 100 sections are closed, then there are only two choices for that class. So, we have:

Number of schedules = 2 x 2 x 3 x 4 = 48

So, there are 48 possible schedules that the student can create from the offerings with two of the math 100 sections closed.

(c) If two of the math 100 sections and four of the English 105 sections are closed, then there are only two choices for math 100 and one choice for English 105. So, we have:

Number of schedules = 2 x 2 x 1 x 1 = 4

So, there are 4 possible schedules that the student can create from the offerings with two of the math 100 sections and four of the English 105 sections closed.

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The total length, in inches, of the four cut boards is 130 inches.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.

We have to find the total length of the board.

Total length of the board is found by adding each length.

Total length = 7½ + 10½ + 9 + 5½

Mixed fraction can be converted to improper fraction by cross multiplication.

7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2

Total length = 15/2 + 21/2 + 9 + 11/2

                    = (15/2 + 21/2 + 11/2) + 9

                     = 47/2 + 9

                     = 65/2

Again improper fraction can be converted to mixed fraction.

Total length of a board = 32 1/2 inches

But there are 4 boards.

Total length of the 4 boards = 4 × 65/2 = 130 inches

Hence the total length is 130 inches.

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The correct classification of the statements is: False, True, False, True.

What is Function ?

Function can be defined in which it relates an input to output.

The point of symmetry on f-¹(x) is (4,6).

False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.

The domain of f-¹(x) is (-∞,4).

True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].

The graphs of f¹(x) and f(x) are reflections across the x-axis.

False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.

The range of f¹(x) is (-∞,∞).

True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).

Therefore, the correct classification of the statements is: False, True, False, True.

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The depth d of the crater is 714 m. The solution has been obtained by using trigonometry.

What is trigonometry?

The area of mathematics known as trigonometry is concerned with the study of the sides, angles, and connections of the right-angle triangle.

We are given a figure which shows that the sun's rays are falling at an angle of 55° and the base is given as 500 m.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = d/500

Here, θ = 55°

So,

⇒tan 55° = d/500

⇒x = 500 tan 55°

⇒x = 500 * 1.428148

⇒x ≈ 714.074

⇒x ≈ 714 m

Hence, the depth d of the crater is 714 m.

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Answer:

13 situps per day

Step-by-step explanation:

To find the number of situps per day, take the total number of situps and divide by the number of days.

39/3

13 situps per day

The expression equivalent to (-√8 -√2) + √-36 is -3√2 + 6i.

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = -1 and both a and b are real numbers.

Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.

The given expression is:

(-√8 -√2) + √-36

The expression can be written as:

(-2√2 - √2) + √(i)²(6)²

Taking the common term:

√2(-2 - 1) + 6i

Simplifying the expression:

-3√2 + 6i

Hence, the expression equivalent to (-√8 -√2) + √-36 is -3√2 + 6i.

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Answer:

true

the t-value does change depending on the number of data points collected.

It is true that the t-value can change depending on the number of data points collected.

The t-value is a statistic used in hypothesis testing to determine whether a sample mean is significantly different from a population mean.

The formula for calculating the t-value includes the sample size (n) in the denominator, which means that as the sample size increases, the t-value decreases (assuming all other factors remain constant).

In other words, a larger sample size will generally result in a smaller t-value, which in turn may affect the interpretation of the results of a hypothesis test. Therefore, the t-value can change depending on the number of data points collected.

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The scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, we have that the original and the dilated figures are given as follows:

Hence the scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.

The problem is incomplete, hence the general procedure to obtain the scale factor was presented.

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The height of the electric pole in order to cast a shadow of 10 m in the same condition as to be 14 m.

The flog poce cast a shadow of 5 metre and itself as a height of 7 m.

Now we have to find the height of an electric pole that will cast the shadow of length 10 m under the same conditions.

The word under the same condition means that the angle of elevation will be same in both the cases, so, we can use the tan theta here,

Tan A = perpendicular/base

Tan A will be equal for both.

Tan A = 7/5

Tan A = H/10

H is the height of the electric pole.

7/5 = H/10

H = 14m

The height of the electric pole will be 14 m.

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50 must have been his starting number of cherries.

Seb had 50 cherries at the start. This can be determined by solving the equation 10x + 5 = 40, where x is the number of days he ate 10 cherries and gave 5 away. When you solve the equation, you get x = 5, meaning he did this 5 times. Since 10x is 50, and 5 is added to that, the total is 50. Therefore, Seb had 50 cherries at the start.

To solve the equation, you first need to subtract 5 from both sides to get 10x = 35. Then, divide both sides by 10 to get x = 3.5. Since Seb could not have eaten 3.5 days worth of cherries, it means that he did the 10 and 5 activity 4 times, giving him 40 cherries before giving away the last 5. So 40 + 5 = 45 and 10x = 50, so 50 must have been his starting number of cherries.

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The vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.

The equation y = -0.25(x - 2)² + 16 models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. We can find the year when the average of couches sold in Germany was the greatest by finding the maximum value of the equation.

To find the maximum value, we can first rewrite the equation in vertex form: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

y = -0.25(x - 2)² + 16

y = -0.25(x² - 4x + 4) + 16

y = -0.25x² + x + 15

To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h), where f(h) is the value of y at the vertex.

h = -b/2a = -1/(2*(-0.25)) = 2

k = f(h) = -0.25(2)² + 2 + 15 = 16

Therefore, the vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.

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A line of reflection in a triangle can be any line that acts as a mirror image, such that the reflected image of the triangle is congruent to the original triangle.

This line is perpendicular to the plane of the triangle and bisects the angle between the two sides that are being reflected.

To be sure that each point was reflected across this line, we apply the reflection rule.

The reflection rule states that the distance from a point to the line of reflection is equal to the distance from its reflection to the line of reflection. This ensures that the reflected image of the triangle is congruent to the original triangle.

In an isosceles right triangle, two of its sides are congruent. This means that it satisfies the Angle-Side-Angle (ASA) congruence theorem. The ASA theorem states that if two triangles have two congruent angles and a congruent side between them, then the two triangles are congruent.

In addition to satisfying the ASA congruence theorem, an isosceles right triangle also satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Finally, the reflection of a triangle is considered a rigid motion, as it preserves the size and shape of the triangle.

Rigid motions do not change the lengths of the sides or the angles between them. They only change the position of the triangle in space. In the case of reflection, the triangle is flipped over the line of reflection, but its size and shape remain unchanged

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Isosceles Right Triangle Reflection to prove ASA Congruence

Answer the following questions:

What line of reflection did you choose for your transformation?

How are you sure that each point was reflected across this line?

What reflection rule did you apply to your triangle?

What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.

Did your triangle undergo rigid motion? Explain why.