A total of $20,000 is invested at an annual interest rate of 6%. No matter how many years this
money is invested, what is the best investment plan to earn the most money in the end?
Compounded continuously
Compounded daily

Compounded quarterly
Compounded monthly

Answer:

z = (2xy-x)

Step-by-step explanation:

Let the first number be x and the other number is z.

According to question,

The average of two number is xy i.e.

[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]

So, the value of z is (2xy-x) i.e. the other number is (2xy-x).

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Answer:

Step-by-step explanation:

012345678910

'yl\f[pt;]p;d[k;ell-=;q'[;

Answer:

see explanation

Step-by-step explanation:

Assuming you mean

secθ × [tex]\sqrt{1-cos^20}[/tex]

= [tex]\frac{1}{cos0}[/tex] × sinθ [ sin²θ + cos²θ = 1 , so sinθ = [tex]\sqrt{1-cos^20}[/tex] ]

= [tex]\frac{sin0}{cos0}[/tex]

= tanθ

= right side , thus verified

Answer:

Step-by-step explanation:

On the graph of two inequalities, solution of two inequalities is defined by the common shaded area.

That means all the points which lie in this area will satisfy both the inequalities.

From the graph attached,

Points given in the options (0, 0), (0, -1) and (1, 1) are not lying in the solution area.

Since, ordered pair given in 4th option is not clear in the picture, Option (4) may be the answer.

Answer: Is reinforced with other material

Step-by-step explanation:

The options are:

A is expensive to build.

B usually cracks under heavy weights.

C looks like any other road.

D is reinforced with other material.

The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.

Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.

Answer:

Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3

Step-by-step explanation:

First, we can graph these inequalities out. As you can see in the picture, the three vertices where the inequalities all connect form a triangle. We can check each of these vertices to find our minimum and maximum.

First, we have (3,7). 4y-3x = 4(7)-3(3)=28-9=19

Next, for (3, -3), we have 4y-3x = 4(-3)-3(3) = -12-9=-21

Finally, for (0.5, 2), we have 4y-3x=4(2)-3(0.5)=8-1.5 = 6.5

Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3

Answer:

0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The manager of a donut store believes that 35% of the customers are first-time customers.

This means that [tex]p = 0.35[/tex]

Sample of 150 customers

This means that [tex]n = 150[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.35[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.35*0.65}{150}} = 0.0389[/tex]

What is the probability that the sample proportion will be between 0.2 and 0.4?

p-value of Z when X = 0.4 subtracted by the p-value of Z when X = 0.2.

X = 0.4

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.4 - 0.35}{0.0389}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

X = 0.2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.35}{0.0389}[/tex]

[tex]Z = -3.85[/tex]

[tex]Z = -3.85[/tex] has a p-value of 0.0001

0.8997 - 0.0001 = 0.8996

0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4

Answer:

6

Step-by-step explanation:

Division yields

[tex]\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}[/tex]

Now for partial fractions: you're looking for constants a, b, and c such that

[tex]\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}[/tex]

[tex]\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a[/tex]

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

[tex]\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}[/tex]

Now, in the integral we get

[tex]\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx[/tex]

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

[tex]\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}[/tex]

Answer:

I started by dividing 2940 by the smallest prime that would fit into it, being 2. This left me with another even number, 1470, so I divided by 2 again. The result, 735, is divisible by 5, but 3 divides in also, and it's smaller, so I divided by 3 to get 245. This is not divisible by 3 but is divisible by 5, so I divided by 5 and got 49, which is divisible by 7.

Answer:

The numbers are 65, 67, and 69

Step-by-step explanation:

Hi there!

We need to find 3 consecutive odd integers.

Consecutive numbers are numbers that follow each other (ex. 1, 2, 3, 4)

We're given that 5 times the first number + 4 times the second + 3 times the third = 800

Let's make the first number x

Since the second number is consecutive to the first and odd, it will be x+2 (Why? Well, let's say x is 5. In that case, x+1=6, which is even. However, x+2=7)

Therefore, the third number is x+4 (once again, if x is 5, x+3=8, but x+4=9)

5 times the first number is 5x

4 times the second is 4(x+2)

3 times the third is 3(x+4)

And of course, that equals 800

As an equation, it'll be:

5x+4(x+2)+3(x+4)=800

open the parenthesis

5x+4x+8+3x+12=800

combine like terms

12x+20=800

Subtract 20 from both sides

12x=780

Divide by 12 on both sides

x=65

The first number is x, so the first number is 65

The second number is x+2, or 65+2=67

The third number is x+4, or 65+4=69

Hope this helps!

Answer:

domain:-16,-8,0,12

range:0,-11,12,14

Answer:

Hypergeometric

Kindly check explanation

Step-by-step explanation:

For a hypergeometric distribution, the following conditions must be met :

1.) The total number of samples must be fixed.

2.) Sample size will be a portion of the population

3.) The probability of success changes per trial. This is because sampling is done without replacement

The above scenario meets the condition described:

Total number of samples = 210

Sample size, n = 10

Blue balls = 200 ; red balls = 10

P(10 red balls)

Using the hypergeometric distribution function and the calculator :

X ~ H(n, N, M)

X ~ (10, 200, 210) = 0.6072

Answer:

8.75 or 8 3/4

Step-by-step explanation:

To do this question, many do it differently. But for now, we will convert the fractions into decimals.

1/4 = 0.25

11/2= 5.5

0.25 + 3 + 5.5

3.25 + 5.5 =

8.75

The answer is 8.75 or 8 3/4

Answer:

Decimal form :

8.75

Step-by-step explanation:

Hope it is helpful....

Answer:

The left side of the histogram has a cluster.

Step-by-step explanation:

The others don't make since.

It's not evenly distributed,

it's not symmetrical, and

it is definitely not a mirror image of the right side.

Answer:

A

Step-by-step explanation:

Answer:

100 lightbulbs

Step-by-step explanation:

Basically find the percentage of lightbulbs that are bad. 5/136. So about 3. 6 percent. I'm going to use a more exact form of this percent for my calculations though. Now use the decimal for of this (0.036....) and multiply it by 2720. Using my exact decimal, the answer just so happened to be exactly 100. So there will be 100 defective lightbulbs per day. (Teachers are a stickler for units, so don't forget them if it's for a teacher)

Hope this helps!

Answer:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Step-by-step explanation:

A

Let's start with the first function:

[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 3, 7, 11, 15...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.

so let's put the two things together:

[tex](-1)^{n}x^{4n+3}[/tex]

Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

So now we can build the whole series:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

B

Now, let's continue with the next function:

[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 5, 9, 13, 17...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.

so let's put the two things together:

[tex](-1)^{n}x^{4n+5}[/tex]

Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

So now we can build the whole series:

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Answer:

pixxer

Step-by-step explanation:

please pick inside please

Answer:

I dont now

Step-by-step explanation:

plz conprendation

Answer:

You can go ahead with this!

Step-by-step explanation:

Option A

Is the write answer

y = -7(-13)

=> y = -7 × (-13)

= y = 91

Answer:

116ML every 3 hours, 928ML a day

Step-by-step explanation:

You said it yourself if there is 29ML in one once and you need 4 ounces every 3 hours then 29 x 4 = 116.

Step-by-step explanation:

I suspect we don't see the full information for the problem here.

all listed 3 methods are typically used to prove that triangles are congruent (= when turned to have the same orientation, they would simply cover each other completely - no overhanging parts from either triangle).

I guess there is a diagram with 2 triangles and what is known about them.

and since we cannot see them, we cannot tell you which method would apply here.

just remember

SSS means all 3 sides of one triangle are exactly the same as the 3 sides of the other triangle. if you know the lengths of all 3 sides, there is only one triangle you can create. you can only orient it differently.

SAS means two sides and the enclosed angle are the same. again, only one triangle can be created with that information.

ASA means one side and the 2 angles at the end points of that side are known. again, only one triangle can be created with that information.

Answer:

y = (-x)^3 - 4

Step-by-step explanation:

Ok, for the function:

y = x^3

When x = 0, we have:

y = 0^3  = 0

So the original graph passes through the point (0, 0)

If we look at the given graph, we can see that the y-intercept (the value of y when x = 0) is:

y = -4

So, this is the graph of y = x^3 moved down 4 units.

You can also see that the graph goes downward as x increases (and up as x decreases) while for the function:

y = x^3

as x increases, we should see that y also increases.

Then we have a reflection across the x-axis.

Ok, now let's describe a vertical shift.

For a general function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

if N is positive, the shift is upwards

if N is negative, the shift is downwards.

And for a function f(x), a reflection across the x-axis is written as:

g(x) = - f(x)

Here we first apply the reflection across the x-axis, so we get:

g(x) = -f(x)

now we apply the shift 4 units downwards

g(x) = - f(x) - 4

replacing f(x) by our function, x^3

we get:

g(x) = -x^3 - 4

And because of the odd power, we can write:

-x^3 = (-x)^3

Then the function is:

g(x) = (-x)^3 - 4

The correct option is the last one.

y = (-x)^3 - 4

Answer:

Let x and y denotes the number of cabinet of the type X and Y. Then given problem can be formulated as, ☝

That is, the second pic

Sketch the region as 3 pic

Step-by-step explanation:

oh the same question was there by xxlunaxx4

Answer:

11422.46

Step-by-step

2300=38000x⁷

x=.669872323

38000*.669872323³=11422.4614

Answer:

24/145

Step-by-step explanation:

Trigonometric identities are equalities involving trigonometric functions and remains true for entire values of the variables involved in the equation.

Some trigonometric identities are:

sin(a + b) = sinacosb + cosasinb; sin(a - b) = sinacosb - cosasinb

cos(a + b) = cosacosb - sinasinb; cos(a - b) = cosacosb + sinasinb

Given that sin a = 3/5. sin a = opposite/hypotenuse.

Hence opposite = 3, hypotenuse = 5. using Pythagoras:

hypotenuse² = opposite² + adjacent²

5² = 3² + adjacent²

adjacent² = 16

adjacent = 4

Given that sin a = 3/5. a = sin⁻¹(3/5) = 36.86

cos a = cos 36.86 = 4/5

cos b = -20/29; b = cos⁻¹(-20/29) = 133.6

sinb = sin(133.6) = 21/29

sin(a + b) = sinacosb + cosasinb = (3/5 * -20/29) + (4/5 * 21/29) = -12/29 + 84/145

sin(a + b) = 24/145