gym offers multiple exercise classes per day. The number of people in an exercise class this week is represented in the list.

3, 6, 8, 7, 2, 4, 5, 10, 7, 14

What is the value of the mode for this data set?

14
8
7
3

Using the lexicographic ordering 5 tuples we get that option b and d is correct.

The lexicographic ordering of 5-tuples means that we compare the elements of each tuple from left to right, and as soon as we find a pair of elements that differ, we say that the tuple with the smaller element is less than the other tuple.

Using this ordering, we can compare the given tuples as follows:

a. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is false because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (a) is not correct.

b. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) < (5,0,101,2,2) is true because the second element of the first tuple (1) is smaller than the second element of the second tuple (0).

Therefore, option (b) is correct.

c. (3,1,10,17,2) < (3,1,10,20,1) is true because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (c) is not correct.

d. (3,1,10,17,2) > (3,1,10,20,1) is false because the fifth element of the first tuple (2) is smaller than the fifth element of the second tuple (1).

(5,1,10,17,2) > (5,0,101,2,2) is true because the second element of the first tuple (1) is greater than the second element of the second tuple (0).

Therefore, option (d) is correct.

So the correct answer is (b) and (d).

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Given the definition above and the fact that top points of the function are at y=9 and the low point are at y=1, the center line must be halfway at y=5.

the amplitude therefore is 4. it's also just half the difference of 1 and 9.

I did this graphically with desmos. Doing it algebraicly would have taken much more time i guess.

Answer:

104

Step-by-step explanation:

Hey There!

So essentially what this problem is asking us to do is solve for the missing angle in a triangle

Remember all of the angles in a triangle will add up to 180

so to find the missing angle we subtract the given angles (38 and 38) from 180

180-38-38=104

so we can conclude that angle A equals 104

Hope this helps!

Answer:

104 degrees

Step-by-step explanation:

Hope this helps!

Have a great day!

Answer:

480 units³

Step-by-step explanation:

Volume of the solid = volume of triangular prism

Volume = base area × height of prism

Base area = ½×b×h

b = 12

h = 5

Base area = ½×12×5 = 30

Height of prism = 16

Volume of the solid = 30 × 16 = 480 units³

Answer:

The product of given binomial and trinomial is:

\(8x^3-34x^2-27x-9\)

Step-by-step explanation:

A binomial is a polynomial with 2 terms and trinomial is a term with 3 terms.

Given

\((4x+3)\\and\\(2x^2-5x-3)\)

Distributive property can be used to find the result.

Writing mathematically

\((4x+3)(2x^2-5x-3)\\= 4x(2x^2-5x-3)+3(2x^2-5x-3)\\= 8x^3-40x^2-12x+6x^2-15x-9\)

Combining alike terms

\(= 8x^3-40x^2+6x^2-12x-15x-9\\= 8x^2-34x^2-27x-9\)

Hence,

The product of given binomial and trinomial is:

\(8x^3-34x^2-27x-9\)

Answer:

The sample system is given below:

see the attached for the graph

The points (1, 2) and (4, -3) are in the intersected region but the point (-2, 8) is outside

Answer:

-52/7 or 7 3/7

Step-by-step explanation:

-5 is also -35/7

2 3/7 is also 17/7

-35/7-17/7 = -52/7

-52/7 = 7 3/7

Answer:

-7 3/7

Step-by-step explanation:

-5 -2 3/7

Factor out the negative sign

-(5 + 2 3/7)

Write as a sum

-(5 + 2 + 3/7)

Calculate

-(7 + 3/7)

Write as a mixed number

-7 3/7

Hope this helps :)

Answer:

790

Step-by-step explanation:

7098uuilu4645

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

The solution of the composite function fog(x) = 3x + 3 at x > 2.

Let the two function f(x) and g(x) generate a new function h(x) using an operation.

The operation is composition of functions and h(x) is a composite function.

We have three piecewise function.

First we have to show that,

the composite function,

fog(x) at x > 2.

For that,

g(x) at x > 2 is,

g(x) = 3x.

Now, f(g(x)),

= f(3x)

= 3x + 3 at x > 2.

Therefore, the function is fog(x) = 3x + 3.

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The complete question:

Find the fog(x) at x > 2

The dot plot shows the number of pairs of shoes that the students have. The total number of students is 16. We would interprete the plot as follows

1 student has 8 pairs

2 students have 9 pairs each

4 students have 10 pairs each

2 students have 11 pairs each

2 students have 12 pairs each

1 student has 13 pairs

1 student has 14 pairs

2 students have 15 pairs each

1 student has 16 pairs

The median is simply the middle value. arranging the pairs, it becomes

8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 13, 14, 15, 15, 16

We can see that the two middle numbers are 11

Therefore, median = (11 + 11)/2 = 11

The correct option is B

Answer:

B. 0.65

Step-by-step explanation:

The closer the r value is to the number 1 or -1, the stronger the correlation.

For example:

0.99 > 0.01

-0.6 > 0.5

.43 < .76

.69 > .21

Please give brainliest and thanks!

Answer:

-4 is not a solution to the following equation.

Step-by-step explanation:

It you replace x with -4 on both sides of the equation you get -2=-12 and they are not equal to each other. Therefore, -4 is not a solution to the equation.

Answer:

A.35

Step-by-step explanation:

trust bro

Answer:D 25

Step-by-step explanation:

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

-3p^8/4q^3

Step-by-step explanation:

<3

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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Answer:

Step-by-step explanation:

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

-108

Step-by-step explanation:

\( - 3 \times { (2 - ( - 4)) }^{2} = \\ - 3 \times ( {2 + 4})^{2} = \\ - 3 \times 36 = - 108\)

Answer:

108 is correct hjgbjbvmbhbjnnn

Answer:

17.1

Step-by-step explanation

a^2+b^2=c^2

2^2 + 17^2 = c^2

4 + 289 = c^2

293 = c^2

square root of 293 or 17.1

Answer: An equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -4x + 20

Step-by-step explanation:

The given equation is in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is 2, which means the line has a slope of 2 and is inclined at an angle of tan^-1(2).

To find an equation of a line that is perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1/2. This means the slope of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is -1/2.

Now we can use the point-slope form of a linear equation to find the equation of the line passing through point P(-6, 4) and having a slope of -1/2. The point-slope form of a linear equation is:

y - y1 = m(x - x1)

Where (x1, y1) is the given point, and m is the slope of the line. So by substituting the values we get:

y - 4 = -1/2(x + 6)

Which can be written as:

y = -1/2x + 4

So the equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -1/2x + 4

Graphing the equations can confirm that the lines are perpendicular as the slope of the first line is 2 and the slope of the second line is -1/2, the product of these slopes is -1 which means they are perpendicular to each other.

Given the points A(3, 4) and B (6, 10), find the pordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.​

we have that

AP/AB=2/(2+1)

AP/AB=2/3

step 1

Find the distance AB in the x-coordinate (ABx)

ABx=6-3=3 units -----> subtract the x-coordinates

we have that

AP/AB=2/3

so

APx/ABx=2/3

APx is the distance AP in the x-coordinate

substitute the given value in the expression above

APx/3=2/3

APx=2 units

Find the x coordinate of point P

Px=AX+APx

Px=3+2=5

step 2

Find the distance AB in the y-coordinate (ABy)

ABy=10-4=6 units (subtract the y-coordinates)

we have that

AP/AB=2/3

so

APy/ABy=2/3

substitute the given value

APy/6=2/3

APy=4 units

Find the y-coordinate of point P

Py=Ay+APy

Py=4+4=8

therefore

Answer: -102

Step-by-step explanation: First we do 9-3 = 6, then add -6 which cancels each other out, so all we have left is -102.

Hope this helps! :)

Answer:

-102

Step-by-step explanation:

(+9) - (+3) = +6

(-6) = -6

+ (-102) = -102

so, +6 -6 -102 = -102

Answer:

Black socks 35

White socks 31

Step-by-step explanation:

Answer:

There is sufficient evidence to support the claim.

Step-by-step explanation:

Given

\(\alpha = 0.10\)

Make A

\(\bar x_1 = 41\)

\(\sigma_1= 4.6\)

\(n = 35\)

Make B

\(\bar x_2 = 45\)

\(\sigma_2 = 4.3\)

\(n = 35\)

First, we state the null and alternate hypothesis

\(H_0 : \mu_1 = \mu_2\)

\(H_1 : \mu_1 \ne \mu_2\)

Next, calculate test statistic:

\(z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}\)

\(z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}\)

\(z = \frac{-4}{\sqrt{0.6046+0.5283}}\)

\(z = \frac{-4}{\sqrt{1.1329}}\)

\(z = \frac{-4}{1.0643}\)

\(z = -3.7583\)

The critical value at \(\alpha = 0.10\) is: \(\±1.282\)

\(-3.7583 < -1.282\)

So, we reject \(H_0\)

This implies that; there is sufficient evidence to support the claim.

There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

Level 1

Step-by-step explanation:

Median of level 1 is  7

Median of level 2 is 9

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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