an average student spend 4½ minutes to read one page of a book. how much time will he need to read 5½ pages?​

*The box plots are shown in the attachment

Answer/Step-by-step explanation:

Range is the difference between the largest value of a data set and the lowest value in that data set.

In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.

For Crackers, the range = 100-70 = 30

For Cookies, the range = 115-70 = 45

Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

\(\dfrac{3}{4}\ miles\)

Step-by-step explanation:

Total distance to a temple = 2 miles

She has walked 1 1/4 miles or 5/4 miles

More miles to reach the hidden temple = total distance - walked distance

\(=2-\dfrac{5}{4}\\\\=\dfrac{8-5}{4}\\\\=\dfrac{3}{4}\)

So, she has to travel \(\dfrac{3}{4}\) miles to reach the hidden temple.

1. The series converges.

2. The series converges.

3. The series diverges.

1. For large enough values of n, we have \($n^5 > \frac{\cos n}{n^7}$\), since \($|\cos n| \leq 1$\). Therefore, we can compare the series to \(\sum_{n=1}^\infty n^5,\) which is a convergent p-series with p=5. By the Direct Comparison Test, our series also converges.

2. We can write the series as \($\sum_{n=1}^\infty \frac{1}{(4^n)^n}$\), which resembles a geometric series with first term a=1 and common ratio \($r = \frac{1}{4^n}$\). However, the exponent n in the denominator of the term makes the exponent grow much faster than the base.

Therefore, \($r^n \to 0$\)as\($n \to \infty$\), and the series converges by the Geometric Series Test.

3.  We can compare the series to \(\sum_{n=1}^\infty \frac{5^n}{6^n},\) which is a divergent geometric series with a=1 and \($r = \frac{5}{6}$\). Then, by the Limit Comparison Test, we have:

\($$\lim_{n \to \infty} \frac{\frac{5^n}{6^n-2n}}{\frac{5^n}{6^n}} = \lim_{n \to \infty} \frac{6^n}{6^n-2n} = 1$$\)

Since the limit is a positive constant, and \($\sum_{n=1}^\infty \frac{5^n}{6^n}$\) diverges, our series also diverges.

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We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Yes, the two cones are congruent because they have the same radius, height, and volume, indicating that they share the same shape and size. Their identical properties provide clear evidence of their congruence.

Congruence means that two objects have the same shape and size. In this case, the cones have the same radius, height, and volume, which are all key properties that determine their shape and size.

To demonstrate their congruence, we can examine the relationships between these properties. Since the cones have the same radius, their circular bases are identical in size. The height of the cones is also the same, meaning their slant heights and lateral surfaces are equal.

Additionally, the volume of a cone is calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height. Given that the volumes of the two cones are equal, it implies that their radii and heights are proportional.

Considering all these factors, we can confidently conclude that the two cones are congruent. Their identical radii, heights, and volumes provide substantial evidence that they share the same shape and size, satisfying the criteria for congruence.

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Nevertheless, it appears that the question is not fully formed; the appropriate request should be:

Answer:

8^18

Step-by-step explanation:

We know that a^b ÷ a^c = a^(b-c)

8^15÷8^−3

8^(15 - -3)

8^(15+3)

8^18

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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Answer:

-7.5

Step-by-step explanation:

I used a calculator

Step-by-step explanation:

- and - makes a + the result will be positive

and now you just do 15.7-8.2=7.5

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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There are 402.28 in2 of pasta in the container.

The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The radius of cylinder (r) = 3.2 inches

Height of cylinder (h) = 14 inches

Height of pasta = 14 – 1.4 = 12.5 inches

Pasta in container = 22/7*(3.2)2*12.5

=402.8 in2

Hence, the container carries 402.8 in2 of pasta in it.

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Answer:

1)
Number of Seats in next three rows: 37, 41, 45

Number of seats in row 21 = 105

2)

Cost for 4, 5, 6 miles:
Miles            Cost($)
4                    14.50

5                    18.00

6                    21.50

Cost for 12 miles = $42.50

Step-by-step explanation:

1) The arithmetic sequence is
25, 29, 33 ....

Each term is 4 more than the previous term

So the next three terms starting with the 4th term area

33 + 4 = 37
37 + 4 = 41

41 + 4 = 45

In terms of the problem statement these are the number of seats in rows 4, 5, 6 respectively

The general equation for an arithmetic sequence nth term is

a(n) = a(1) + d(n - 1)

Here a(1) is the first term; here a(1) = 25

d = difference between successive terms called the common difference; here common difference = 4

n is of course the number of terms to be considered

using the values we have
a(n) = 25 + 4(n- 1)

= 25 + 4n - 4

= 21 + 4n

So the 21st term is a(21)

a(21) = 21 + 4 (21)

= 21 + 84

= 105

------------------------------------------

2. Another arithmetic sequence

The first term is the charge for the first mile = 4

The second term = 7.5 for 2 miles

The third term = 11.5 for 3 miles

So d = 11 - 7.5 = 7.5 - 4 = 3.5

The cost for 4 miles = 11 + 3.50 = $14.50

The cost for 5 miles = 14.50 + 3.50 = $18

The cost for 6 miles = 18 + 3.50 = $21.50

Using the equation for finding the nth term we get

a(n) = a(1) + d(n - 1)
a(n) = 4 + 3.5(n-1)

a(n) = 4 + 3.5n - 3.5

a(n) = 0.5 + 3.5n

We have the following table

Miles            Cost      ($)

1                     4.00

2                    7.50

3                    11.00

4                    14.50

5                    18.00

6                    21.50

For 12 miles which would correspond to the 12 term

a(12) = 0.5 + 3.5(12)

= 0.5 + 42

= $42.50

Step-by-step explanation:

♡︎♡︎♡︎♡︎♡︎♡︎♥︎♥︎♡︎♥︎

Answer:

y - x = - 5

Step-by-step explanation:

Applying the rule gives

x = \(\frac{1}{3}\) × 36 + 9 = 12 + 9 = 21

y = \(\frac{1}{3}\) × 21 + 9 = 7 + 9 = 16

Thus

y - x = 16 - 21 = - 5

Answer:

lateral area = side area = (10 x 6 x 2) + (14 x 10 x 2) = 400 in²

total surface area = lateral area + top & bottom area = 400 + (14 x 6 x 2) = 568 in²

Answer:

19.5 or 19 1/2

Step-by-step explanation:

2 2/3 = 2.6666666666666667

52/ 2 2/3 = 19.5

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

22+b = t

Step-by-step explanation:

22+b= t, where t is the total number of books in the past two months.

Answer:

m = $14/day

w = $6/day

Step-by-step explanation:

See attached image.

Answer:

4*10-2, 4, 40%, 1/4, 0.004

Step-by-step explanation:

4*10-2=38

1/4=.25

4=4

.004=.004

40%=.40

The to your question is that we can use the normal distribution to estimate the probability that the product will last between 16.536 and 8.054 years.


In this case, we want to calculate the probability for x = 16.536 and x = 8.054. The mean (μ) is 14.242 years, and the standard deviation (σ) is 3.978 years.

Using the formula, we can calculate the z-scores for both values:
For x = 16.536: z = (16.536 - 14.242) / 3.978
For x = 8.054: z = (8.054 - 14.242) / 3.978

Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator. Subtracting the probability for the lower z-score from the probability for the higher z-score will give us the probability that the product will last between 16.536 and 8.054 years.

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Answer:

-66

Step-by-step explanation:

11 × (-6) = -66

Answer:

85 minutes to complete the whole triathlon.

Step-by-step explanation:

The lowest point of the graph shows 85 minutes.

Hope this helps!

Answer:

According to the graph we can determine that it took Payton C) 85 minutes to finish the swimming and biking parts of the triathlon.

Step-by-step explanation:

We can see where the graph ends, this is where Payton finishes the swimming and biking parts of the triathlon. The lowest point of the graph on the y axis (Her Total Time in Minutes) is 85 minutes, therefore we can determine it took her 85 minutes. Hope this helped :) Good luck!

Answer:

A

Step-by-step explanation:

no duh also her scores ARE overall higher

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

2. c

3.

a. no

b. yes

c. yes

d. no

e. yes

I think this is right

4.

Part A;

5.4-3.1=D

Part B;

4.9+3.1=t

Part C:

1. 2.3

2. 8

I hope this helps!!!

Step-by-step explanation:

The answer to the given problem is Relative maximum

(x, y) = `(-1, -1)` relative minimum (x, y) = `(1, 3).

Given function is `g(x) = x² + 2/x`.

To find the relative maxima and minima of the given function g(x),

we will use the first and second derivative tests as follows.

First derivative test:

`f′(x) = 2x – 2/x²`

The critical points of g(x) are the roots of the derivative:

`f′(x) = 2x – 2/x² = 0

We will multiply the equation by `x²` to clear out the fraction:`

2x³ – 2 = 0`Therefore, `x³ = 1`.

That is, the critical values of x are: `

x = 1, -1, 0`.

So the critical points are:

`(0,0), (1,3), (-1, -1)`.

We will now compute the second derivative of g(x):`

f″(x) = 2 + 4/x³`

Second derivative test:

We need to determine the sign of the second

derivative near each critical point.

Then, the conclusions are:

If `f″(x) > 0`, then `f(x)` has a relative minimum at x.

If `f″(x) < 0`, then `f(x)` has a relative maximum at x.

If `f″(x) = 0`, then we cannot make a conclusion.

The second derivative at `x = 0` is positive:

`f″(0) = 2 + 4/0³ = undefined.`

So, `f(x)` has no relative extreme at x = 0.

The second derivative at `x = 1` is: `f″(1) = 2 + 4/1³ = 6 > 0`.

Therefore, `f(x)` has a relative minimum at x = 1.

The coordinates of this relative minimum are:

Relative minimum (x, y) = `(1,3)`.

The second derivative at `x = -1` is: `f″(-1) = 2 + 4/(-1)³ = -6 < 0`.

Therefore, `f(x)` has a relative maximum at x = -1.

The coordinates of this relative maximum are:

Relative maximum (x, y) = (-1, -1).

So, we have Relative maximum (x, y) = `(-1, -1)`

and Relative minimum (x, y) = (1, 3).

Hence, the answer to the given problem is Relative maximum

(x, y) = `(-1, -1)` relative minimum (x, y) = `(1, 3).

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Polygons are shapes that have the following:

-sides are all straight

-no overlapping

-shape is always closed

Hope this helps :)

Answer:I don't know

Step-by-step explanation:do the work