5,6,8,9,7 find the mean,median and mode​

number of eighth-graders who want fruit smoothies: 150

total number of students: 800

relative frequency: 150/800 = 3/16 ≈ 0.19

Answer:

a. 2.5

b. x = 17.5 because 7 times 2.5 = 17.5

Step-by-step explanation:

4 times 2.5 = 10

2 times 2.5 = 5

:)

Answer:

Not a parallelogram.

Step-by-step explanation:

By the midpoint formula, the midpoint of a segment between \((x_{0},\, y_{0})\) and \((x_{1},\, y_{1})\) is:

\(\begin{aligned} \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)\end{aligned}\).

A quadrilateral is a parallelogram if and only if the midpoints of the two diagonals are the same.

The two diagonals of quadrilateral \({\sf ABCD}\) are segment \(\sf{AC}\) and segment \({\sf BD}\), respectively.

Using the midpoint formula, the midpoint of segment \({\sf AC}\) (between \({\sf A}\; (3,\, 3)\) and \({\sf C}\; (-3,\, 1)\)) would be:

\(\begin{aligned} & \left(\frac{3 + (-3)}{2},\, \frac{3 + 1}{2}\right) \\ =\; & (0,\, 2)\end{aligned}\).

Likewise, the midpoint of segment \({\sf BD}\) (between \({\sf B}\; (1,\, 2)\) and \({\sf D}\; (-1,\, 4)\) would be \((0,\, 3)\).

Thus, quadrilateral \({\sf ABCD}\) would not be a parallelogram since the midpoints of its two diagonals are not the same.

The completed blanks are

From the question, we have the following parameters that can be used in our computation:

The table of values

The rise is the difference between y values

So, we have

Rise = 6.2 - 3.1 = 3.1

For the run, we have

Run = 3 - 2.25 = 0.75

So, we have

Slope = 3.1/0.75

Slope = 4.13

Hence, the slope is 4.13

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ita 3 fiths x plus three eigths

Answer: 11.25 kmph or 6.99 mph

Step-by-step explanation:

take the speed equation s=d/t (speed equals distance over time)

s=72/6.4 (15 min is 0.4 of an hour)

your final answer will be S= 11.25 kilometers per hour or 6.99 miles per hour

From the consequence of intersecting secant theorem, we have that

Hence, b = 44°

If the coordinates of point A are (- 6, 1) and the coordinates of M are

(- 2, 3) then coordinates of B are (2, 5).

A midpoint of a line (x, y) divides a line segment into two equal parts

by the formula x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2.

Given, Point M is the midpoint of AB.

The coordinates of point A are (- 6, 1) and the coordinates of M are (- 2, 3).

Therefore, The coordinates of point B are,

- 2 = (- 6 + x₂)/2 and 3 = (1 + y₂)/2.

- 4 = - 6 + x₂ and 6 = 1 + y₂.

x₂ = 2 and y₂ = 5.

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Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

Answer:

Assuming that the scale is 1, x int: (-4,0), y int: (0,-3)

Step-by-step explanation:

Hope this helps :)

Answer:

point A

Step-by-step explanation:

on the number line, point A represent -2

Answer:

The possible answer should be 15 teaspoons

b. Cannot be determined

b. The triangle have one congruent angles and one congruent sides, this is not enough information to conclude that they are congruent triangles.

Answer:

Perimeter: 4+\(\pi \\\) mm

Area: \(\pi\) mm^2

Step-by-step explanation:

Perimeter:

90/360 * 4\(\pi \\\) +2 + 2 = 4+ \(\pi \\\)

Area:

90/360 * 4\(\pi\) = \(\pi\)

Answer: 7.14 mm and 3.14 mm²

Step-by-step explanation:

The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of \(2\pi r\), where r is the radius and \(\pi\) is an irrational constant, approximately 3.14.

Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is \(\frac{1}{4}* 2\pi r\) or \(\frac{1}{2} \pi r\). The radius is 2 mm, so this value is

\(\frac{1}{2} \pi*2=\pi\)

However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is

\(2+2=4\)

By adding \(\pi\) to 4 we get \(\pi +4\) or 7.14 mm.

The  area is the total space enclosed by a figure. The total area of a whole circle is \(\pi r^2\), where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or \(\frac{1}{4} \pi r^2\). We can plug in 2 for r and solve to get the area.

\(\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi\)

Hence, the area is \(\pi\), or around 3.14 mm².

The correct statements for comparing the effectiveness of the SAT preparation program are the 3rd, 4th, 5th, 6th statements.

The statements in order are

Since, school counselor want to compare effectiveness of SAT preparation program with response variable will be the improvement in SAT score.

We can consider this as a improvement assessment, so that the initial abilities of each student will be different. With this we can see the improvement from student with bad initial score, and for the student that has a good score in initial exam they barely to have improvement.

For example student A have initial score 600 and student B have initial score 1300 after preparation program student A have final score 1200 and student B have final score 1350. In the example, we can see 200% improvement from student A and only 4% improvement from student B.

Also, with matching pair design that based on variable, we can see the variability in improvement making it easier to know the effectiveness of SAT preparation program than the randomized design.

Thus, the correct statements is the 3rd, 4th, 5th, 6th statements.

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The Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5.

What is trigonometric function ?

Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate degree angle of a triangle.

The difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
hence , Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5

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A 96% confidence interval for the mean difference in textbook prices at the two online bookstores is (3.22,8.38).

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

The mean and standard deviation are M = 5.8 and s = 4.658

To calculate the estimated standard error, we apply

S = \(\sqrt{s^2/n}\)

 =\(\sqrt{4.658^2/5}\)

= 2.08

The 96% confidence interval is :

CI = x ±t₉₆s/√n

= 5.8 ±2.7764× 2.08/√5

= 5.8±2.58

= (3.22,8.38)

Hence, a 96% confidence interval for the mean difference in textbook prices at the two online bookstores is (3.22,8.38).

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we can infer that the firm is currently maximizing its profit. Option (b), "the firm is currently maximizing its profit," is the most appropriate inference from the provided data.

To determine whether the firm is maximizing its profit, we need to analyze the relationship between marginal revenue (MR), marginal cost (MC), and price. In a monopolistically competitive market, firms aim to maximize their profit by producing at a level of output where MR equals MC.

From the information provided, we know that the firm's marginal revenue is equal to $15 and marginal cost is also equal to $15. This indicates that the firm is producing at the level where its marginal revenue equals its marginal cost, which is a characteristic of profit maximization.

Additionally, we are told that the firm is charging the highest price it can at $30. This means that the firm is able to set its price above its average total cost, resulting in a positive difference between price and average total cost, known as economic profit.

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The two statements that are true about the company's Market share going from 50 to 65 percent of the total market . The initial market share and multiply by 100, which gives 30 percent. Option B is correct answer.

The two statements that are true about the company's market share going from 50 to 65 percent of the total market are:

The company's market share increased by 30 percent: The difference between the initial market share of 50 percent and the final market share of 65 percent is 15 percentage points. To calculate the percentage increase, we can divide the difference by the initial market share and multiply by 100, which gives (15/50) x 100 = 30 percent.

The company's relative market position improved: With a market share of 65 percent, the company now holds a greater proportion of the total market than before. This means that its relative market position has improved compared to its competitors, who have a smaller share of the market. This could translate into increased bargaining power, profitability, and other benefits for the company.

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a company’s market share went from 50 to 65 percent of the total market. of the following choices, which two statements about the company's market shares are true?
A) 40

B) 30

C) 35

D) 45

Answer:  The correct answer is x = 19 / 5

Step-by-step explanation:

Solve the equation

5x + 3 = 22

Subtract 3 from both sides

5x + 3 − 3 = 22 − 3

5x = 19

Divide both sides by 5

5x/5 = 19/5

x = 19 / 5

Answer: About 94% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature.

The correlation coefficient, r, is 0.969.

Step-by-step explanation:

The correct set of statements is:

About 94% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature. The correlation coefficient, r, is 0.969.

The \(r^2\) value, also known as the coefficient of determination, indicates the proportion of the variation in the dependent variable (beach visitors) that can be explained by the independent variable (daily temperatures). In this case, a \(r^2\) value of 0.9382 means that approximately 93.82% of the variation in beach visitors can be explained by the variation in daily temperatures.

The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between the two variables. The statement correctly states that the correlation coefficient, r, is 0.969, which indicates a strong positive linear relationship between beach visitors and daily temperatures.

Therefore, the set of statements "About 94% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature. The correlation coefficient, r, is 0.969." is true based on the given information.

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The slope of the line representing the relationship between the price of the salad and its weight in ounces is 0.25 tells you that the price of the salad increases by $0.25 for every additional ounce of salad.

The slope of the line representing the relationship between the price of the salad and its weight in ounces is 0.25.

The slope represents the rate of change of the price of the salad with respect to its weight is $0.25 per ounce.

The slope tells you that the price of the salad increases by $0.25 for every additional ounce of salad.

If you want to purchase a salad weighing x ounces the cost of the salad would be $0.25 times x or $0.25x.

If you want to purchase a salad weighing 10 ounces, the cost would be $0.25 times 10 is $2.50.

Similarly, if you want to purchase a salad weighing 25 ounces the cost would be $0.25 times 25 is $6.25.

The graph shows a proportional relationship between the weight of the salad and its price with a constant rate of change represented by the slope of the line.

As the weight of the salad increases the price also increases proportionally.

The y-intercept of the line represents the cost of the salad when it weighs zero ounces is not applicable in this context.

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The common difference between successive terms in this sequence is -0.1.

The common difference between successive terms in a sequence is the constant value that is added or subtracted to each term to obtain the next term in the sequence. To find the common difference in the given sequence, we need to subtract each term from the term that follows it.
Subtract the first term (0.36) from the second term (0.26): 0.26 - 0.36 = -0.1
Subtract the second term (0.26) from the third term (0.16): 0.16 - 0.26 = -0.1
Subtract the third term (0.16) from the fourth term (0.06): 0.06 - 0.16 = -0.1
Based on the calculations, the common difference between successive terms in this sequence is -0.1. Therefore, the correct answer is a) -0.1.

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Answer:

40

Step-by-step explanation:

The spinner gives you 5 choices.

The die gives you 8 choices

Answer: The total number of choices is 5* 8 = 40

it is saying that You spin a spinner with five equal spaces so, we have 5

roll an eight - sided die so, we have 8

then, it is saying that

How many possible outcomes are in the sample space

= 5 × 8

= 40

Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

The probability of the next child being a girl is 0.33.

What  is probability?

Probability is defined as how likely it is for an event to happen or for a statement to be true.

Main Body:

Total children = 3

Total girl child = 1/3 of total children

                       =(1/3)*3

                       = 1

Therefore total boys = 2

Probability of next child being girl = 1/3

                                                         =0.33

hence the answer is 0.33.

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The best estimate of the product is b) 1 times 10.

The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.

Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.

Correct Question :

Which expression is the best estimate of the product of (7/8)8(1/10)?

a) 0 times 8

b) 1 times 10

c) 7 times 8

d) 1 times 8

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The factored form of x² + 10x + 25 is (x + 5)².

To determine two values of n that allow the polynomial x² + nx + 25 to be a perfect square trinomial, we need to consider the general form of a perfect square trinomial:

(ax + b)² = a²x² + 2abx + b²

Comparing this form with the given polynomial x² + nx + 25, we can see that:

a²x² = x² (So, a = 1)

2abx = nx (So, 2ab = n)

b² = 25 (So, b = ±5)

Since we have b = ±5, the values of n can be obtained by substituting b = 5 and b = -5 into 2ab = n.

For b = 5:

2(1)(5) = n

10 = n

For b = -5:

2(1)(-5) = n

-10 = n

The two values of n that allow the polynomial x² + nx + 25 to be a perfect square trinomial are n = 10 and n = -10.

Now let's factor the polynomial x² + nx + 25 using one of the determined values of n (let's use n = 10 as an example):

x² + 10x + 25

We can factor this trinomial as a perfect square trinomial:

(x + 5)²

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