Combine Like Terms. 7x - 5x

Answer:

Step-by-step explanation:

hello

{1,2,3,4,5} ∪ {2,4,6,8,10} = {1,2,3,4,5,6,8,10}

hope this helps

Answer:

{1, 2, 3, 4, 5, 6, 8, 10}

Step-by-step explanation:

Union of the sets is the combination of the elements in the two sets.

{1, 2, 3, 4, 5}  ∪  {2, 4, 6, 8, 10}

{1, 2, 3, 4, 5, 6, 8, 10}

Answer:

0.15 or 15%

Step-by-step explanation:

If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.

To calculate how much the price went up each day on average, we will create exponential equation.

x = price of the stock

y = average daily change

[tex]x*y^{4} =1.75x[/tex]  divide by x

[tex]y^{4} = 1.75[/tex]

We will calculate it using logarithms.

y = 1.15016, rounded to 1.15

We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%

Answer:

a surface of a cone looks like an hyperbolic cylinder

Answer:

(See explanation below for further details).

Step-by-step explanation:

The procedure for plotting each line consists in creating a table with at least two different points, given that Euclidean Geometry states that any line can be created with only two points,  and plotting the lines with the help of graphing tools:

(a) [tex]y = \frac{2}{3}\cdot x - 5[/tex]

(i) Table of values

       x              y

      -2         -6.333

      -1          -5.667

       0             -5

       1          -4.333  

       2         -3.667      

(ii) Plotting the line

The line is presented below in the attachment "line_1".

(b) [tex]6\cdot x - 2\cdot y + 5 = 0[/tex]

[tex]2\cdot y = 6\cdot x +5[/tex]

[tex]y = 3\cdot x +\frac{5}{2}[/tex]

(i) Table of values

       x              y

      -2           -3.5

      -1            -0.5

       0            2.5

       1             5.5  

       2            8.5    

(ii) Plotting the line

The line is presented below in the attachment "line_2".

Answer:

CL = LD

Step-by-step explanation:

In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?

1) (CL)(LD)=AB

2) AL > LB

3) CL = LD

4) BL > AB

Answer: The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L.

Since CD is bisected at point L, CL = LD

Also CD = 2CL = 2LD

Answer:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Step-by-step explanation:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.  

Question:  

Use the generalized binomial expansion to expand (1 + x)^a up to the a = 5 and hence  determine (1.05)^5. to 5 decimal places.

Answer:

Using the binomial theorem

[tex](1 .05)^5 = 1.27628[/tex]

Step-by-step explanation:

The binomial theorem is given by

[tex](a +b)^n = \binom{n}{0} a^nb^0 + \binom{n}{1} a^{n-1}b^1....+ \binom{n}{n} a^0b^n[/tex]

For the given case, we have

[tex]a = 1 \\\\b = 0.05 \\\\n = 5 \\\\[/tex]

So,

[tex](1 +0.05)^5 = \binom{5}{0} (1)^5(0.05)^0 + \binom{5}{1} (1)^4(0.05)^1 + \binom{5}{2} (1)^3(0.05)^2 + \binom{5}{3} (1)^2(0.05)^3 + \binom{5}{4} (1)^1(0.05)^4 + \binom{5}{5} (1)^0(0.05)^5[/tex]

[tex](1 +0.05)^5 = (1)(1)^5(0.05)^0 + (5) (1)^4(0.05)^1 + (10) (1)^3(0.05)^2 + (10) (1)^2(0.05)^3 + (5) (1)^1(0.05)^4 + (1) (1)^0(0.05)^5[/tex]

[tex](1 +0.05)^5 = 1 + 0.25 + 0.025 + 0.00125 + 0.00003125 + 0.0000003125[/tex]

[tex](1 + 0.05)^5 = 1.27628[/tex]

Therefore, using the binomial theorem

[tex](1 .05)^5 = 1.27628[/tex]

Answer: The width of the garden is 6 Meters

Step-by-step explanation:

3x + x = 24

The length is 3x and the width is x

24 / 4 = 6

x= 6

The width of the garden is 6 Meters

Answer:

x = 6

Step-by-step explanation:

3x + x = 24

24 / 4 = 6

x = 6

Answer:

The provement is below

Step-by-step explanation:

z^(1/2)=x^(1/2)+y^(1/2)  =>  (z^(1/2))^2=  (x^(1/2)+y^(1/2))^2

=> z=x+y+2*x^(1/2)*y^(1/2) => z-x-y= 2*x^(1/2)*y^(1/2)

=> (z-x-y)^2= (2*x^(1/2)*y^(1/2) )^2 => (z-x-y)^2=4*x*y           (1)

Pls note that (z-x-y)^2= ((-1)*(-1)*(z-x-y))^2= ((-1)*(x+y-z))^2= (-1)^2*(x+y-z)^2=

=(x+y-z)^2

So  (z-x-y)^2= (x+y-z)^2 !!! Substitute in (1) (z-x-y)^2 by (x+y-z)^2   and will get

the required equality  (x+y-z)^2=4*x*y

Answer:

Step-by-step explanation:

Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]

As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]

Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

Answer:

A ∪ B = {1,3,6,9,12,15,18,24}

Step-by-step explanation:

Let A = {3,6,9,12,15}

B = {1,6,12,18,24}

So,

A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}

A ∪ B = {1,3,6,9,12,15,18,24}

Answer:

{1,3,6,9,12,15,18,24}

Step-by-step explanation:

The union is joining of the elements of the sets

{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}

= {1,3,6,9,12,15,18,24}

Answer:

8 is in the hundreds place as well as in the tens place.

Step-by-step explanation:

We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.

Answer:

The probability of getting even 7 times out of 8 is 1/256. Hope this helps!!

Step-by-step explanation:

21/7 = 3 is the answer of your question

Answer:

left 2 units and up 6 units

Step-by-step explanation:

f(x) = (x + 2)^4 + 6

y = f(x) + C  C > 0 moves it up

So this moves it up 6 units

y = f(x + C) C > 0 moves it left

So this moves it to the left 2 units

The parent function g(x) is shifted to the left 2 units and up 6 units to get the function f(x).

Function is a type of relation, or rule, that maps one input to specific single output.

Given function;

f(x) = (x + 2)^4 + 6

y = f(x) + C  

C > 0 moves it up

So, this moves it up 6 units.

y = f(x + C)

C > 0 moves it left

So, this moves it to the left 2 units.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ2

Answer:

The decision is to not reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50% (P-value = 0.1443).

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of all those using the drug that experience relief is significantly higher than 50%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.54.

[tex]p=X/n=108/200=0.54[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.54-0.5-0.5/200}{0.035}=\dfrac{0.038}{0.035}=1.061[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.061)=0.1443[/tex]

As the P-value (0.1443) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of all those using the drug that experience relief is significantly higher than 50%.

Answer: Hope this helps <3

Step-by-step explanation:

Graphs can be used to represent functions.

See attachment for the graphs of [tex]\mathbf{x^2 + y = 2}[/tex] and [tex]\mathbf{x^2 + y^2 = 9}[/tex]

The functions are given as:

[tex]\mathbf{x^2 + y = 2}[/tex]

[tex]\mathbf{x^2 + y^2 = 9}[/tex]

Rewrite [tex]\mathbf{x^2 + y^2 = 9}[/tex] as:

[tex]\mathbf{x^2 + y^2 = 3^2}[/tex]

The above equation represents a circle of radius 3, and that has its center as the origin.

Similarly, we have:

[tex]\mathbf{x^2 + y = 2}[/tex]

Make y the subject

[tex]\mathbf{y = 2 -x^2}[/tex]

Rewrite as:

[tex]\mathbf{y = -x^2 + 2 }[/tex]

The above is a square function, that is reflected over the y-axis, and then shifted up by 2 units.

See attachment for the graphs of [tex]\mathbf{x^2 + y = 2}[/tex] and [tex]\mathbf{x^2 + y^2 = 9}[/tex]

Read more about graphs and functions at:

https://brainly.com/question/18806107

Answer:

17.1 meters

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

6 and 16 are the legs, because they form the right angle. c is the hypotenuse because it is opposite the right angle.

[tex]6^2+16^2=c^2[/tex]

Evaluate the exponents.

6^2= 6*6= 36

16^2= 16*16= 256

[tex]36+256=c^2[/tex]

Add 36 and 256.

[tex]292=c^2[/tex]

Since c is being squared, take the square root of both sides of the equation. The exponent and square root will cancel and leave c by itself

[tex]\sqrt{292} =\sqrt{c^2}[/tex]

[tex]\sqrt{292}=c[/tex]

[tex]17.0880075=c[/tex]

Round to the nearest tenth. The 8 in the hundredeth place tells us to roung the 0 in the tenth place up to a 1.

[tex]17.1=c[/tex]

c= 17.1 m

The missing length, or the hyptenuse is 17.1 meters.

Obtain the next iterate by plugging the previous iterate into the function.

First iterate:

[tex]z_0=2+i\implies z_1=f(z_0)=(2+i)^2-2-2i=1+2i[/tex]

Second iterate:

[tex]z_2=f(z_1)=(1+2i)^2-2-2i=-5+2i[/tex]

Third iterate:

[tex]z_3=f(z_2)=(-5+2i)^2-2-2i=19-22i[/tex]

Fourth iterate:

[tex]z_4=f(z_3)=(19-22i)^2-2-2i=-125-838i[/tex]

Answer:

B.

Step-by-step explanation:

According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.

So in this case to find x, you would do the Sin(L)=x/y

Answer:

B.  Sin(L)=x/y  indeed!

Step-by-step explanation:

Answer:

a. [tex]N(1)=2600[/tex]

b. [tex]N'(a) = 470/a[/tex]

c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)

d. lim a→[infinity] N′(a) = 0

Step-by-step explanation:

a.

the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:

[tex]N(1)=2600 + 470ln(1)[/tex]

[tex]N(1)=2600 + 470*0[/tex]

[tex]N(1)=2600[/tex]

b.

To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:

[tex]N'(a) = 2600' + (470ln(a))'[/tex]

[tex]N'(a) = 0 + 470*(1/a)[/tex]

[tex]N'(a) = 470/a[/tex]

c.

The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).

The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.

d.

When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.

Answer:D

Step-by-step explanation:

Answer:

Sales

Step-by-step explanation:

Since it is mentioned that the store mistakenly priced an item at $20 instead of $30 so there is a difference of $10 so the price of sales is increased by $10 due to mispricing the value of the item so that it would be recorded at $30 rather than $20

Therefore in the given case neither it is considered as a loss nor an operating expense but as a sales and the same is to be relevant

Hence, the given options are incorrect

Answer:

$282.98

Step-by-step explanation:

For computing the principal amount we need to apply the present value function i.e to be shown in the attachment below:

Data provided that in question

Future value = $25,000

Rate of interest = 9%

NPER = 13 years × 4 quarters =  52 quarters

PMT = $0

The formula is shown below:

= -PV(Rate;NPER;PMT;FV;type)

So, after applying the above formula, the present value is $282.98

Step-by-step explanation:

firstly firstly we have to suppose f(X) as y and then solve it by interchanging X and y.

hope this is helpful

Answer:

B

Step-by-step explanation:

To find inverse you switch f(x) and x use y for f(x) then solve for y.

1. x = 2y - 8

2. x + 8 = 2y

3. (x + 8) / 2 = y

4. 1/2x + 4 = y

Hey there! :)

Answer:

f(15) = 29 ft.

Step-by-step explanation:

We can write an arithmatic equation for this pattern:

Where:

[tex]n_{1}[/tex] = 1, [tex]n_{2}[/tex] = 3

Find the rate of change. This is constant because this is an arithmatic sequence.

3 - 1 = 2.

We can begin to write an explicit function for this situation:

f(n) = [tex]n_{1}[/tex] + d(n-1) where d is the rate of change:

f(n) = 1 + 2(n-1)

Substitute 15 for n to solve for the distance traveled after 15 seconds:

f(15) = 1 + 2(15-1)

f(15) = 1 + 2(14)

f(15) = 1 + 28

f(15) = 29 ft.

Therefore, the distance traveled after 15 seconds is 29 ft.

Answer:

8 and 4/9 i think... i am sorry if i am wrong

Step-by-step explanation:

Answer:

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]

[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]

= 875.5

Next is to find the population variance;

[tex]V = \frac{875.5}{8}[/tex]

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

[tex]Sd = \sqrt{109.4375}[/tex]

Standard deviation, Sd = 10.4612

To find the sample variance;

[tex]V = \frac{875.5}{8-1}[/tex]

[tex]V = \frac{875.5}{7}[/tex]

Variance, V = 125.0714

The sample variance is;

[tex]Sd = \sqrt{125.0714}[/tex]

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.

Answer:

C. 20.67

Step-by-step explanation:

I got it right on edge :)

Answer:

[tex]\$45[/tex]

Step-by-step explanation:

[tex]20+(2.5*20)=45[/tex]

Marking up means that the new value is added onto the original value.

As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%

Answer:

20*2.5 = $50 Gross margin $70 Selling price

Step-by-step explanation: