The length of a rectangle is four times its width.
If the perimeter of the rectangle is 70 yd whats the length and width

The stem-and-leaf display of the data is

Stem | Leaves

1 | 2

2 | 2

3 | 3

4 | 5, 8

To start, let's assume we have a set of data values, such as 12, 22, 33, 45, 48, 53, 61, 62, 72, 83, 91, 96, 99.

The stem-and-leaf display consists of two parts: the "stem" and the "leaf." The stem represents the leading digit(s) of the data values, and the leaf represents the trailing digit(s). For example, the number 12 has a stem of 1 and a leaf of 2.

Now, let's organize the data values into their corresponding stems:

Stem 1: 12

Stem 2: 22

Stem 3: 33

Stem 4: 45, 48

Next, we list the leaves corresponding to each stem. The leaves are listed in ascending order next to their respective stems:

Stem 1: 2

Stem 2: 2

Stem 3: 3

Stem 4: 5, 8

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The answer is (B) 3.

To find the relative extrema of f on the open interval (-4, 4), we need to find the critical points of f, which are the values of x where f'(x) = 0 or f'(x) is undefined.

First, we set f'(x) = 0:

f'(x) = (3 - 2x - x^2)sin(2x - 3) = 0

This equation is satisfied when either sin(2x - 3) = 0 or 3 - 2x - x^2 = 0.

When sin(2x - 3) = 0, we have:

2x - 3 = nπ, where n is an integer.

Solving for x, we get:

x = (nπ + 3)/2

There are two solutions to this equation on the interval (-4, 4), namely:

x = -1.07 and x = 2.57

When 3 - 2x - x^2 = 0, we have:

x^2 + 2x - 3 = 0

Using the quadratic formula, we get:

x = (-2 ± sqrt(16))/2

x = -1 or x = 3

However, x = -1 is not in the interval (-4, 4), so we only need to consider x = 3.

Therefore, the critical points of f on the interval (-4, 4) are x = -1.07, 2.57, and 3.

To determine whether these critical points are relative maxima or minima or neither, we need to use the second derivative test.

The second derivative of f is given by:

f''(x) = (6x - 4)sin(2x - 3) - (3 - 2x - x^2)cos(2x - 3)(2)

At x = -1.07, we have:

f''(-1.07) = (6(-1.07) - 4)sin(2(-1.07) - 3) - (3 - 2(-1.07) - (-1.07)^2)cos(2(-1.07) - 3)(2)

f''(-1.07) = -9.83

Since f''(-1.07) is negative, the critical point x = -1.07 is a relative maximum.

At x = 2.57, we have:

f''(2.57) = (6(2.57) - 4)sin(2(2.57) - 3) - (3 - 2(2.57) - (2.57)^2)cos(2(2.57) - 3)(2)

f''(2.57) = 11.41

Since f''(2.57) is positive, the critical point x = 2.57 is a relative minimum.

At x = 3, we have:

f''(3) = (6(3) - 4)sin(2(3) - 3) - (3 - 2(3) - (3)^2)cos(2(3) - 3)(2)

f''(3) = -12

Since f''(3) is negative, the critical point x = 3 is a relative maximum.

Therefore, f has 3 relative extrema on the open interval (-4, 4), namely, 2 relative minima and 1 relative maximum.

The answer is (B) 3.

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Step-by-step explanation:

Find differences in year (x)

x=2050-2015

x=35 years

Find total percentage

=2.5%×(x)

=2.5×35

=87.5%

Multiply percentage with initial number

=87.5%×380000

=33250000

The correct answer is not provided in the given options. The sun would not be visible at noon on December 21 in a city at 60°N latitude.

The angle of the sun above the horizon at noon on December 21 depends on the latitude of your city. Since you mentioned that you live at 60°N, we can determine the angle using some knowledge about the tilt of the Earth and the seasons.

On December 21, the winter solstice, the Northern Hemisphere is tilted away from the sun. This means that the angle of the sun above the horizon at noon is lower than on other days of the year.

To calculate the angle, we need to subtract the latitude of your city (60°N) from the tilt of the Earth (23.5°).

So, the angle of the sun above the horizon at noon on December 21 in your city would be:
23.5° - 60° = -36.5°

The negative sign indicates that the sun is below the horizon at noon on December 21. Therefore, the correct answer is not provided in the given options. The sun would not be visible at noon on December 21 in a city at 60°N latitude.

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Answer:

13, 24, and 34

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 24, 34, . . .

0+ 1 = 1

1+ 1 = 2

2+ 1 = 3

3+ 2 = 5

5+ 3 = 8

8+ 5 = 13

13+ 8 = 24

24+ 13 = 34

start at 1, then add the number behind it to move forward one space. repeat process.

Answer:

1. $155 ≥ $31.50p + $13.25

2. p ≤ 4

The correct answer is option E which is Cos ( 70 ) = \(\dfrac{LN}{8}\).

The complete question is attached with the answer below:-

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

As we can see from the figure that ∠L = 70 and ∠M = 20 We can see that the length LN will be calculated as:-

Cos 70 = Base / Hypotenuse

So for an angle of 70, the base is LN and the hypotenuse is equal to 8 units.

Cos 70 = LN = 8

Therefore the correct answer is option E which is Cos ( 70 ) = \(\dfrac{LN}{8}\).

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Answer:

A & E

Step-by-step explanation:

Jus took it on edge

ANSWERS

• f'(x) = 18x⁵ + 32x³ - 6x² + 8x - 4

• f'(c) = -4

EXPLANATION

To find the derivative of this function we can apply the product rule,

In this case, the functions are,

• g(x) = x³ + 2x

• h(x) = 3x³ + 2x - 2

The derivative of g(x) is,

The derivative of h(x) is,

So, the derivative of f(x) is,

Let's simplify the answer. Multiply the two parts in the first term,

Add like terms,

Do the same for the second term,

Add like terms,

Hence, the derivative of f(x) is f'(x) = 18x⁵ + 32x³ - 6x² + 8x - 4.

Now, we have to find the value of f'(0). Note that all the terms of f'(x) except for the last one contain x, so they all are 0 except for the last term. Hence, the value of f'(0) is -4

Answers in bold

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \boldsymbol{0.5}\\\cline{1-2}6 &3\\\cline{1-2}10 & \boldsymbol{5}\\\cline{1-2}16 & \boldsymbol{8}\\\cline{1-2}25 & \boldsymbol{12.5}\\\cline{1-2}n & \boldsymbol{0.5n}\\\cline{1-2}\end{array}\)

========================================================

Explanation:

The given table looks like this

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \\\cline{1-2}6 & 3\\\cline{1-2}10 & \\\cline{1-2}16 & \\\cline{1-2}25 & \\\cline{1-2}n & \\\cline{1-2}\end{array}\)

Focus on the row that has two values in it.

x = number of rolls = 6

y = number of people 3

k = constant of proportionality

y = kx

k = y/x = 3/6 = 0.5

The constant of proportionality is k = 0.5 which gives the direct variation equation of y = 0.5x

If x = 1, then y = 0.5*1 = 0.5 meaning that 1 roll feeds 0.5 people. This means we need 2 rolls to feed one person.

If x = 10, then y = 0.5x = 0.5*10 = 5 people can be fed with those 10 rolls. This process is continued until we finish filling out the table.

The series ∑((-1)⁽ⁿ⁻¹⁾ * 5n)/(6n) from n = 1 to infinity converges based on the alternating series test.

To test the series for convergence or divergence using the alternating series test, we need to check if the terms of the series alternate in sign and if their absolute values decrease as n increases.

The series is given by:

∑((-1)⁽ⁿ⁻¹⁾  * 5n)/(6n) from n = 1 to infinity

Let's analyze the terms of the series:

Alternating sign: The terms alternate between positive and negative because of the (-1)⁽ⁿ⁻¹⁾ factor.

Decreasing absolute values: We can simplify the terms by canceling out the common factors of 5 and 6:

((-1)⁽ⁿ⁻¹⁾  * 5n)/(6n) = (-5/6)ⁿ

The absolute values of the terms are decreasing because

|(-5/6)ⁿ| < |(-5/6)⁽ⁿ⁻¹⁾ | for all n.

Since the series satisfies the conditions of the alternating series test, namely alternating sign and decreasing absolute values, we can conclude that the series converges.

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Answer:

20.27

Step-by-step explanation:

\(\sqrt{411} =20.27\)

Answer:

The square root of 411 cannot be simplified. √411 is already in its simplest radical form.

Step-by-step explanation:

Answer:

\(\frac{23\sqrt{10} }{10}\)

Step-by-step explanation:

\(\frac{3}{\sqrt10} }+\sqrt{40} \\\frac{3*\sqrt{10} }{\sqrt{10} *\sqrt{10} } +\sqrt{40} \\\frac{3\sqrt{10} }{\sqrt{10*10} } +\sqrt{40} \\\frac{3\sqrt{10} }{10} +2\sqrt{10} \\\frac{3\sqrt{10} }{10}+\frac{2\sqrt{10} }{1} \frac{*10}{*10} \\\frac{3\sqrt{10} }{10}+\frac{20\sqrt{10} }{10} \\\frac{3\sqrt{10}+20\sqrt{10} }{10}\\\frac{23\sqrt{10} }{10}\)

Hope this helps you.

Let me know if you have any other questions :-)

A) The average velocity of the particle from t=0s to t=1s is 4 m/s.

B) The average speed from t=0s to t=1s is 4 m/s.

The position of a particle as a function of time is given by x=(6m/s)t+(−2m/s²)t².

A) To find the average velocity of the particle from t=0 to t=1s, we can use the formula:

average velocity = change in position / change in time

The change in position from t=0 to t=1s is:

x(1s) - x(0s) = [(6m/s)(1s) + (-2m/s²)(1s)²] - [(6m/s)(0s) + (-2m/s²)(0s)²]

= 4m

The change in time is:

1s - 0s = 1s

Therefore, the average velocity is:

average velocity = change in position / change in time = 4m / 1s = 4m/s

B) To find the average speed from t=0 to t=1s, we need to find the total distance traveled by the particle from t=0 to t=1s. The distance traveled is the magnitude of the change in position, which is always positive. Therefore, we can use the formula:

average speed = total distance traveled / change in time

The total distance traveled from t=0 to t=1s is:

| x(1s) - x(0s) | = | [(6m/s)(1s) + (-2m/s²)(1s)²] - [(6m/s)(0s) + (-2m/s²)(0s)²] |

= | 4m | = 4m

Therefore, the average speed is:

average speed = total distance traveled / change in time = 4m / 1s = 4m/s

Note that the average velocity and average speed are the same in this case because the particle is moving in a straight line and its displacement and distance traveled are in the same direction.

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The null hypothesis is that there is no significant difference in the number of words remembered between the group that texted during the audio clip and the group that did not. The symbol "H0" represents the null hypothesis.

Based on the texting and concentration scenario, let's identify the null hypothesis and what "p" represents in it.
Null hypothesis (H0): There is no significant difference in the number of words remembered by students when they are texting versus when they are not texting during the audio clips. In other words, texting has no effect on concentration.

The null hypothesis is a statistical assumption that says there is no statistical significance in a group of observations. Hypothesis testing is used to test the reliability of a hypothesis using sample data. It is sometimes called "blank" and stands for H0. The null hypothesis, also known as the Conjecture is used in quantitative analysis to test a theory about business, investment, or the economy to determine whether the idea is true or false.

In this hypothesis, "p" represents the difference in the proportions of words remembered while texting and not texting. If p = 0, it means there is no difference in the students' concentration between the treatment (texting) and control (not texting) groups.

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Answer:

no

Step-by-step explanation

an example of vertical angles would be 6 and 8

pls give brainliest :)

Answer:180

Step-by-step explanation:

hope this helps

Answer:

0.8 mm

Step-by-step explanation:

Given that you require the actual size.

The ant has been magnified by 15 X

To find the actual size divide magnified size by 15

actual size = 12 mm ÷ 15 = 0.8 mm

Answer:

The roots of the of the function are 2,3 and 4.

Step-by-step explanation:

The given function is

f(x) = x³ - 9x² + 26x - 24

It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).

According to the remainder theorem if a function is divided by (x-c), then the remainder is equal to f(c). If f(c) is equal to 0, therefore c is the root of the function.

Use synthetic method to divide f(x) by (x-2).

f(x) = (x - 2) (x² - 7x + 12)

f(x)= (x - 2) (x² - 4x - 3x + 12)

f(x)= (x - 2) (x(x - 4) - 3(x - 4))

f(x)= (x - 2) (x - 4) (x - 3)

To find the roots equation the function equate the function equal to 0.

0 = (x - 2) (x - 4) (x - 3)

Equate each factor equal to 0.

x = 2,3,4

Therefore the roots of the function are 2,3 and 4.

(btw this is someone else's answer i found since i got a little confused myself heh)

Answer:

The roots of the of the function are 2,3 and 4.

Step-by-step explanation:

\The roots of the of the function are 2,3 and 4.

The equation of the linear function passing through the points in the table is y = -2x - 1.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the data in the table, we pick two points, (1,-3) and (2,-5).

First, we determine the slope:

\(m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{-5-(-3)}{2 - 1} \\\\m = \frac{-5+3}{2 - 1} \\\\m = \frac{-2}{1}\\ \\m = -2\)

Now, we choose one (1, -3) and slope m = -2, and substitute the values into the point-slope form equation:

y - y₁ = m( x - x₁ )

y - (-3) = -2( x - 1 )

Simplify

y + 3 = -2x + 2

y = -2x + 2 - 3

y = -2x - 1

Therefore, the linear function is y = -2x - 1.

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The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Step-by-step explanation:

area of ∆ is 10in².

hope this helps you.

The number of poker hands consisting of 2 aces and 3 kings is 41,472.

The probability that the first king is dealt out on the 13th card is 1/52.

(a) There are 4 aces and 4 kings in a standard deck of playing cards, so there are C(4,2) = 6 ways to choose 2 aces out of 4, and C(4,3) = 4 ways to choose 3 kings out of 4. Then, there are C(48,3) = 17, 296 ways to choose the remaining 3 cards from the remaining 48 cards in the deck. The number of poker hands consisting of 2 aces and 3 kings is 6 * 4 * 17, 296 = 41,472.

(b) The probability that the first king is dealt out on the 13th card is 1/52, since there are 52 cards in a standard deck and the first king can be any of them. The probability that the first king is dealt out on the 13th card is independent of the order in which the other cards are dealt, so this is the final answer.

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Answer: D. The number of digital subscriptions increases by 3.4% each year

C. the number of digital subscriptions increases by 103.4% each month.

the probability that he drove the small car is 0.890 (option A).

Using Bayes' theorem to solve the problem given, let us represent the following events:

A: Friend drives the small carB: Friend drives the large carC: Friend is on timeGiven that three-quarters of the time he drives the small car and one-quarter of the time he drives the large car, we can calculate the prior probabilities:

P(A) = 3/4 and P(B) = 1/4.

Also, given that he usually has little trouble parking with probability 0.9 when driving the small car and is on time with probability 0.6 when driving the large car, we can calculate the likelihoods:

P(C|A) = 0.9 and P(C|B) = 0.6

Using Bayes' theorem, we can calculate the posterior probability of driving the small car given that he was on time on a particular morning:

P(A|C) = P(C|A) * P(A) / (P(C|A) * P(A) + P(C|B) * P(B))= 0.9 * 3/4 / (0.9 * 3/4 + 0.6 * 1/4) = 0.890

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Answer:

-60

Step-by-step explanation:

s=-105+45

=-60

hope it helps

This model is typically used to model relationships between two variables that are exponentially related. The log-log model can be used to estimate the parameters of an exponential relationship between the two variables.

A log-log model is a type of nonlinear regression model where both the response and predictor variables are transformed into natural logs. This model is used to model the relationships between two variables that are exponentially related. The log-log model is used to estimate the parameters of an exponential relationship between the two variables. To use a log-log model, the data must first be transformed into natural logs. This transformation is accomplished by taking the natural log of both the response and predictor variables. Once the data is in log form, a nonlinear regression model can be used to estimate the parameters of the exponential relationship between the two variables. The model is then fit to the transformed data, and the parameters of the exponential relationship can be estimated. The estimated parameters can then be used to make predictions about the relationship between the two variables.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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a) The relation is reflexive, symmetric, and transitive.

b) The relation is not reflexive, symmetric, or transitive.

a) For each watermelon x, x is related to x because the measured weight of x is at least the measured weight of x. Therefore, the relation is reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is also related to x (meaning the measured weight of y is at least the measured weight of x). Therefore, the relation is symmetric.

For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is related to z (meaning the measured weight of x is at least the measured weight of z). Therefore, the relation is transitive.

b) For each watermelon x, x is not related to x because no two watermelons have the same measured weight. Therefore, the relation is not reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is not related to x (meaning the measured weight of y is not at least the measured weight of x).

Therefore, the relation is not symmetric. For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is not related to z (meaning the measured weight of x is not at least the measured weight of z).

Therefore, the relation is not transitive.

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Answer:

Step-by-step explanation:

for vertex

x-2=0 gives x=2

when x=2,y=4

vertex (2,4)

axis of symetry

x-2=0