the length of a rectangle is 3 more than twice its width. the total area of the rectangle is 54 square units. what is the width and length of the rectangle?

Step-by-step explanation:

a. To find dy/dx when y = 2xlog e (2x), we can use the chain rule. First, we rewrite the function as y = 2x(ln(2x) + 1) where ln is the natural logarithm. Then, we can take the derivative of y with respect to x:

dy/dx = 2(ln(2x) + 1) + 2x(1/2x) = 2ln(2x) + 2 + 2/x

b. To find f′(0) when f(x) = e^x^2/e^x+1, we can take the derivative of the function with respect to x:

f′(x) = (2xe^x^2(e^x+1) - e^x^2(e^x+1)) / (e^x+1)^2

Setting x = 0, we get:

f′(0) = 2e^0(e^0 + 1) - e^0(e^0 + 1) / (e^0 + 1)^2 = 1 / (e^0 + 1)^2 = 1 / 2^2 = 1/4

Answer:

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

The scale factor is 2, since each side is twice the initial length.

There are 4 congruent copies, as we can see on the picture.

The dilated area is 12*4 = 48 square units, since the area is the product of two dimensions, each dimension is twice the initial value therefore the area is 2*2 = 4 times greater.

To select a sample from the population of 24 math 152 students, I used stratified random sampling.

Stratified random sampling is when a population is divided into groups or strata, then a random sample is taken from each group. In this case, the population of 24 students was divided into two groups of 12. The first group was selected by randomly assigning each student a number from 1-12, then I used a random number generator to choose numbers from 1-12. The numbers that were chosen were the subjects for the first group. I repeated this process for the second group of 12, assigning each student a number from 13-24, then using the random number generator to choose the subjects for the second group. I repeated this process until I had a sample of 10 students. This process allowed me to create a sample that was representative of the entire population.

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Answer:

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

Translate each wording to mathematical expression and compare with the given 18 = 3 × 6.

A) 18 is 3 times as many as 6:

B) 18 is 2 times as many as 9:

C) 3 is 6 times as many as 18:

D) 6 is 3 times as many as 18:

To find the maximum height the ball achieves before landing, we need to find the vertex of the parabola represented by the equation h(t) = -16t^2 + 59.2t + 114.24. The vertex form of a parabola's equation is y = a(x-h)² + k where (h, k) is the coordinates of the vertex.

We can get the vertex form by completing the square of x term.

h(t) = -16t² + 59.2t + 114.24

h(t) = -16(t² - 3.68t) + 114.24 + 3.68t

h(t) = -16(t-0.92)² + 118.92

The maximum height is 118.92 ft which is k.

Uday Tahlan

Answer:

a) (-2,0) is the x-intercept of the line.

b) (0,4) is the y-intercept of the line.

c) "2" is the slope of the line.

d) 2x + 4 = y (Equation of the Line)

Step-by-step explanation:

All linear equations have a general form: mx+n.

When we figure out two points on the line, we can use them in this general formula and find out the equation for the line.

We can use x and y intercepts of the line for that, they are also asked to find.

The x-intercept of the line is (-2,0) because this is where the line crosses the x axis, this point is named as x-intercept.

Except the axis, y-intercept has no more difference than x-intercept. So, the y-intercept of a line is where the line crosses the y axis.

We can see that the line crosses y axis at (0,4).

Now, we know two specific points on the line. This means that we can find the slope and write the equation for this line.

We can find the slope using the formula below:

y1 - y0 / x1 - x0 = Slope

This would give us the slope for the line, no matter which point you take as (x1, y1). The order is not important.

If you use the given points on the formula above, you would get "2" as the slope of the line.

In the general form of a linear equation, the coefficient of "x" is equal to the slope of the line. This means that "m" is equal to "2". (y = 2x + n)

Finally, you can use one of the known points to find out the real equation for the line.

Let's use (0,4):

2x + n = y (Use 0 for "x" and 4 for "y" variable.)

We can conclude that "n" is equal to 4.

So, the equation of this line is equal to "2x + 4 = y".

The required equation in which case the left side is the power of 10 times n and the right side is the result of multiplying 0.1515 by 10 will be' (10)n = 10(0.1515).

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the equation as;

(10)n=10(0.11515 -n=0.1515

(10)n = 10(0.1515).

n = 0.1515

Therefore, the resulting equation from the subtraction as;

(10n - n) = 10(0.1515) - 0.1515

9n = 9 (0.1515).

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The test statistic of -0.03 is compared to a critical value to determine if the null hypothesis can be rejected. If the test statistic is less than or equal to the critical value, the null hypothesis is rejected and the 90% figure is not accurate.

Calculate the sample proportion:

Sample Proportion

= 657/750

= 0.87

Calculate the test statistic:

Test Statistic

= 0.87 - 0.90

= -0.03

Compare the test statistic to a critical value:

If the test statistic is less than or equal to the critical value, then we can reject the null hypothesis. If the test statistic is greater than the critical value, then we cannot reject the null hypothesis.

The null hypothesis is that the percentage of adults in the region who drink milk is equal to 90%, while the alternative hypothesis is that the percentage is not equal to 90%. A sample of 750 adults is polled and the sample proportion is calculated to be 0.87.

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Answer:

Step-by-step explanation:

30-12/3=d

d=drinks he bought

$30-$12=$18

$18/$3=6

he got 6 drinks

Answer:

1, 3, 5, 7 and 19

Step-by-step explanation:

to find the first 4 terms, substitute n = 1, 2, 3, 4 into the rule, then

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 - 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

the first 4 terms are 1, 3, 5, 7

to find the 10th term , substitute n = 10 into the rule

a₁₀ = 2(20) - 1 = 20 - 1 = 19

[tex]dy/dt[/tex] for each pair of functions is [tex]4t^3 + 28t[/tex].

[tex]y[/tex] = [tex]x^2 - 2x[/tex]

[tex]x[/tex] = [tex]t^2 + 8[/tex]

[tex]y[/tex] = [tex](t^2+8)^2 - 2(t^2+8)[/tex]

[tex]dy/dt[/tex] = [tex]2(t^2+8)(2t) - 2(2t)[/tex]

         = [tex]4t^3 + 32t - 4t[/tex]

[tex]dy/dt[/tex] = [tex]4t^3 + 28t[/tex]

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable. The function closest to that input value is best approximated linearly by the tangent line.

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For the figure shown in the image having TV as the midsegment, the length of TV is 40

When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.

In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.

For the given figure, the proportionate sides are

UV and TV, UW and WX

Calculating for s

UV / TV = UW / WX

1 / (-2s + 42) = 2 / (3s + 77)

cross multiplying

3s + 77= 2(-2s + 42)

3s + 77= -4s + 84

collecting like terms

3s + 4s = 84 - 77

7s = 7

s = 1

solving for TV

= -2s + 42

= -2 * 1 + 42

= 40

the value of TV is 40

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Answer:

Step-by-step explanation:

You need a sample size of at least 1612 recent liberal arts major graduates to have a margin of error of 400 with a 90% confidence level.

What is standard deviation ?

The standard deviation is a measure of the spread or dispersion of a set of data. It is a statistical measure that describes how much variation or deviation there is from the mean (average) of a set of values. The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences of each value from the mean.

n = (z*sigma / E)^2

where , n = sample size

z = the z-score corresponding to the desired level of confidence (90% confidence level corresponds to a z-score of 1.645)

sigma = the estimated standard deviation of starting salaries (9000)

E = the desired margin of error (400)

Plugging in the known values ,

n = (1.645 * 9000 / 400)^2

n ≈ (40.1125)^2

n ≈ 1611.6

So you need a sample size of at least 1612 recent liberal arts major graduates to have a margin of error of 400 with a 90% confidence level.

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The number of ways of dealing a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit is 2,593,812

What is the combination?

In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.

In order to find the number of ways of dealing with a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit, we can use the combination formula.

The combination formula is used to find the number of ways to select a certain number of items from a larger group without regard to order.

First, we need to find the total number of ways to select 5 cards from a 52-card deck.

This is given by the combination formula: nCr = n! / (r!(n-r)!)

Where n is the total number of items (52) and r is the number of items to be selected (5).

So, nCr = 52! / (5!47!) = 2, 598, 960

Now we need to subtract the number of ways to select a hand that doesn't contain at least one card of each suit.

We can select 4 cards from one suit and only one card from another suit in 4C1 * 48C4 ways = 448454239/24 = 5148.

Now we can subtract this number from the total number of ways to select 5 cards from a 52-card deck to find the number of ways to select a five-card hand that contains at least one card in each suit:

2598960 - 5148 = 2,593,812

Hence, the number of ways of dealing a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit is 2,593,812

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There are 7!/3! ways for 8 people to sit around a circular table if Alice, Bob, and Eve do not want to sit next to each other.

Rotation is the process of rotating an object in two or three dimensions around an axis. This axis can be a point in space, a line, or a plane. Rotation can also refer to a continuous change of direction, such as the rotation of the Earth around its axis. Rotation can be described using terms such as clockwise, counterclockwise, and angular velocity. Rotation can also be described using mathematical equations, such as Euler's rotation theorem. Rotation can be used to create symmetry in design, or to create motion in an animation.

This is because we can pick any of the 7 people to be seated first, then any of the 6 people to be seated second, then any of the 5 people to be seated third, and so on. However, since Alice, Bob, and Eve do not want to sit next to each other, we must divide the 7! by 3! to account for the fact that the order in which Alice, Bob, and Eve are seated does not matter. The 3! accounts for the fact that we could arrange the three of them in 3! = 6 different orders. Therefore, the total number of ways for 8 people to sit around a circular table if Alice, Bob, and Eve do not want to sit next to each other is 7!/(3!) = 840 ways.

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A translation is a mapping of a figure in a direction and distance without changing its orientation. The rule for a translation is of the form (x, y) -> (x + h, y + k), where h and k are the horizontal and vertical distances of the translation, respectively.

A reflection is a mapping of a figure across a line, called the line of reflection, without changing its size or orientation. The rule for a reflection is of the form (x, y) -> (x, -y) or (x, y) -> (-x, y), depending on whether the line of reflection is horizontal or vertical, respectively.

A rotation is a mapping of a figure around a point, called the center of rotation, by a certain angle. The rule for a rotation is of the form (x, y) -> (x', y'), where x' and y' are the coordinates of the rotated point, and are given by x' = xcos (theta) - ysin(theta) and y' = xsin(theta) + ycos(theta), where theta is the angle of rotation.

A glide reflection is a composition of a translation and a reflection. The rule for a glide reflection is of the form (x, y) -> (x + h, -y) or (x, y) -> (x, -y + k), depending on whether the line of reflection is horizontal or vertical, respectively, and h or k is the distance of translation.

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Portus has four 1-cent stamps, three 5-cent stamps, and three 25-cent stamps. 79 different postage amount of at least one cent can postbus make.

We can get the sums of 1 cent, 2 cents, 3 cents and 4 cents by combining one 1-cent coin, two 1-cent coins, three 1-cent coins and four 1-cent coins, respectively. i.e., 4 different sums.

We can get three sums of 5 cents, 10 cents, and 15 cents by combining mean five-cent coins., i.e. 3 different sums.

 we can get three sums of 25 cents, 50 cents, and 75 cents by combining means twenty-five-cent coins. i.e,3 different sums.

Now,

4*3 = 12 different sums by combining 4 one-cent coins with 3 five-cent coins.

Again,  

Now,

add all these combinations:

    4 + 3 + 3 + 12 + 12 + 9 + 36 = 79.

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98 degrees is approximately equal to 5.48 radians.

How to convert degree measure to radian measure?

To convert a degree measure to a radian measure, you can use the conversion factor of 180/π.

98 degrees is equal to (98*π)/180 radians

So, 98 degrees is approximately equal to 5.48 radians.

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Answer: I think it is the first one

Step-by-step explanation:

Answer:

I'm pretty sure it's x^2 - 4x

Step-by-step explanation:

Check the picture below.

The statements that are true about the triangle f d e and its dilated counterpart f' d' e' are: (1) The center of dilation was (0, 0). (2) The coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). (3) f' d' e' is a similar triangle to f d e.

The triangle f d e and its dilated counterpart f' d' e' have specific properties that make them similar triangles. The center of dilation for the transformation was (0, 0). This means that the distance from the center of dilation to each point before and after the dilation was the same. The coordinates of triangle f d e were (negative 9, 3), (negative 9, 9), and (negative 6, 6). In order to obtain the coordinates of f' d' e', the dilation rule one-third(x,y) (one-third x, one-third y) was used. This means that the x and y coordinates of each point were divided by three. The result is that the new coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). These new coordinates demonstrate that the triangle f d e and its dilated counterpart f' d' e' are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

The smallest bouncy prime is 2.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.

A number n is said to be a bouncy prime if it is prime, and the sum of the positive divisors of n (also known as the sum of divisors function, denoted f(n)) is also prime.

The smallest prime number is 2. The sum of divisors of 2 is

1+2 = 3

which is also prime, so 2 is a bouncy prime.

Since 2 is the smallest prime and it is a bouncy prime, the smallest bouncy prime is 2.

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The number of ways in which exactly one of the toddler triplets to end up with their coat is given as follows:

3.

A sample space is a set that contains all possible outcomes in the context of an experiment.

The cardinality of the sample space in this problem, considering the Fundamental Counting Theorem, is obtained as follows:

N = 3 x 2 x 1

N = 6.

(the first chosen has 3 possible options, the second has two and the third has one).

The six possible outcomes are given as follows, considering the order Red - Green - Blue:

Hence there are three outcomes for exactly one of the toddler triplets to end up with their coat.

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The rate of change of the volume at that particular instant is - 62.8 m^3/h.

How to get the rate of change of the volume?

First, we can write the dimensions as:

radius = R = (5m + 1m/h*t)

height = H = (8m - 4 m/h*t)

Where t is the time in hours.

Then the volume of the cylinder will be:

V = pi*R^2*H = 3.14*(5m + 1m/h*t)^2*(8m - 4 m/h*t)

To get the rate of change, we need to differentiate it with respect to t, we will get:

V' = 3.14*(2*(5m + 1m/h*t)*(1m/h)*(8m - 4 m/h*t) + (5m + 1m/h*t)^2*(-4m/h))

V' = 3.14*( (2 m/h)*(5m + 1m/h*t)*(8m - 4 m/h*t) - (4m/h)*(5m + 1m/h*t)^2)

V' = 3.14*(2m/h)*( (5m + 1m/h*t)*(8m - 4 m/h*t) - 2*(5m + 1m/h*t)^2)

As you can see the rate of change depends on t, but we want the rate of change at this instant, then we use t = 0, replacing that on the above equation we get:

V'(0) = 3.14*(2m/h)*( (5m + 1m/h*0)*(8m - 4 m/h*0) - 2*(5m + 1m/h*0)^2)

V'(0) = 3.14*(2m/h)*( (5m)*(8m ) - 2*(5m)^2)=  -62.8 m^3/h

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Answer:

can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2

Linear Inequality

A Linear Inequality is like a Linear Equation (such as y = 2x+1) ...

... but it will have an Inequality like <, >, ≤, or ≥ instead of an =.

Answer:

Step-by-step explanation:

[tex]x^{2} -7x+c=(x+a)^{2}[/tex]

[tex]x^{2} -7x+c=x^{2} +2ax+a^{2}[/tex]

[tex]-7x=2ax\\a=-7/2[/tex]

[tex]a^{2} =c\\c=(-7/2)^{2} =49/4[/tex]

Step-by-step explanation:

You will get the x and y interceptions by substituting. To make it easier, put x=0 , 3, -3 and solve the equation.

Hope this helps you.