Solve of the following equations for x: 3x = 5

Rewrite the limit as

[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]

Answer:

-5 < x < 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let, present age of son be 'x'

present age of father be 'y'

y = 4x→ equation ( i )

After five years,

Son's age = x + 5

father's age = y + 5

According to Question,

[tex]y + 5 = 3(x + 5)[/tex]

Put the value of y from equation ( i )

[tex]4x + 5 = 3(x + 5)[/tex]

Distribute 3 through the parentheses

[tex]4x + 5 = 3x + 15[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S. and change its sign

[tex]4x - 3x = 15 - 5[/tex]

Collect like terms

[tex]x = 15 - 5[/tex]

Calculate the difference

[tex]x = 10[/tex]

Now, put the value of X in equation ( i ) in order to find the present age of father

[tex]y = 4x[/tex]

plug the value of X

[tex] = 4 \times 10[/tex]

Calculate the product

[tex] = 40[/tex]

Therefore,

Present age of son = 10

present age of father = 40

Hope this helps..

Best regards!!

Answer:

Pretty sure it is c

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

She will be painting the outsides of the table, so we need to find the surface area of the table.

There is the flat part of the table, which is a rectangular prism. There are also four legs, which are rectangular prism.

So, she will paint C. the surface area of 6 rectangular prisms.

Hope this helps!

Answer:

j/2+7= -12

(j+14)/2= -12

cross-multiply

j+14= -24

j= -38

Answer:

[tex]\boxed{j=-38}[/tex]

Step-by-step explanation:

[tex]\frac{j}{2} +7=-12[/tex]

Subtract 7 on both sides.

[tex]\frac{j}{2} +7-7=-12-7[/tex]

[tex]\frac{j}{2}=-19[/tex]

Multiply both sides by 2.

[tex]\frac{j}{2}(2)=-19(2)[/tex]

[tex]j=-38[/tex]

Answer:

No correlation

Step-by-step explanation:

Hey there! :)

This has no correlation because all the points are spread out throughout the graph making no correlation.

Answer:

D no correlation

Step-by-step explanation:

too many scattered dot all over the place if its some going up down its NO CORRELATION!!!

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

            Hi my lil bunny!

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Let's solve this step by step.

[tex]2^x + 4^x + 8^x = -14[/tex]

              ↓

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

    Prime number 2 to the power of 2 = 4                

[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]

                    ↓

Prime number 2 to the power of 3 = 8

[tex]2^x + 2^2x + 2^3x = -14[/tex]

                    ↓

We need to exponentiate the power.

The following rule is applied:

           [tex](A^B) ^C = A^BC[/tex]

In our example,

   A is equal to 2,

   B is equal to 2 and

   C is equal to x.

[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]

                         ↑

In order to solve this non-linear equation, we need to move all the terms to the left side.

In our example,

- term −14, will be moved to the left side.

Notice that a term changes sign when it 'moves' from one side of the equation to the other.

___________________

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, there are no negative expressions.

                                  ↓

            [tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

366 Minutes

Step-by-step explanation:

Hey there! I'm happy to help!

Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.

10x+50y=1080

x+y=28

We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.

x+y=28

Subtract x from both sides.

y=28-x

Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.

10x+50(28-x)=1080

We use distributive property to undo the parentheses.

10x+1400-50x=1080

We combine like terms.

-40x+1400=1080

We subtract 1400 from both sides.

-40x=-320

We divide both sides by -40.

x=8

Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.

Have a wonderful day! :D

Answer:

x = 88

Step-by-step explanation:

The sum of the angles in a triangle add to 180

47+45 +x = 180

Combine like terms

92+x = 180

Subtract 92 from each side

92+x-92= 180-92

x =88

Answer: sample required n = 18

Step-by-step explanation:

Given that the value under under null hypothesis is 40 while the value under the alternative is less than 40, specifically 35.9

∴ H₀ : u = 40

  H₁  : u = 35.9

therefore β = ( 35.9 - 40 ) = -4.1

The level of significance ∝ = 0.05

Probability of committing type 11 error P = 0.1

standard deviation α = 5.8

Therefore our z-vales (z table)

Z₀.₅ = 1.645

Z₀.₁ = 1.282

NOW let n be sample size

n = {( Z₀.₅ + Z₀.₁ )² × α²} / β²

n = {( 1.645 + 1.282 )² × 5.8²} / (- 4.1)²

n = 17.14485

Since we are talking about sample size; it has to be a whole number

therefore

sample required n = 18

According to the given situation, the computation of two number in a given ratio is shown below:-

We assume the numbers is x and y

Given that

[tex]\frac{x}{y} = \frac{3}{1}[/tex]

x = 3y

and

[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]

With the help of above formula we will put the value and be able to find the values of x and y

x - y = 6

3y - y = 6

2y = 6

y = 3

x = 3y = 9

x = 9, y = 3

Therefore the correct answer is x = 9 where as y = 3

It's 1000 charges and not 1.000 charges

Answer:

A)Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = 1.4286

C) p-value = 0.15628

D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges

Step-by-step explanation:

We are given;

x = 1002 charges

s = 14

μ = 1000 charges

n = 100

degree of freedom = n - 1 = 100 - 1 = 99

A) The hypotheses are;

Null Hypothesis;H0: μ = 1000

Alternative Hypothesis;Ha: μ ≠ 1000

B) t-statistic = (x - μ)/(s/√n)

(1002 - 1000)/(14/√100) = 1.4286

C) From the t-score calculator results attached, the p-value is approximately 0.15628

D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.

Answer:

Step-by-step explanation:

The surface area of a cone is:

● Sa = Pi*r^2 +Pi*r*l

r is the radius and l is the slant heigth

The diameter of this cone is 12 inches so the radius is 6 (12/2=6).

●Sa = Pi*36 +Pi*6*10

●Sa = 301.59 in^2

Answer:

pi (6) * 10+ pi ( 6)^2

Step-by-step explanation:

The surface area of a cone is given by

SA =  pi rl +pi r^2  where r is the radius and l is the slant height

We know the diameter is 12 so the radius is 12/2 = 6

SA =  pi (6) * 10+ pi ( 6)^2

Answer: 4 years after the original investment, it is approximately $1,093.

Step-by-step explanation:

Hi, to answer this question we have to apply the simple interest formula:  

I = p x r x t

Where:  

I = interest

P = Principal Amount  

r = Interest Rate (decimal form)  

t= years

Replacing with the values given  

I = 1000x (2.25/100) x t

I = 1000x (2.25/100) x 3 =67.5

1000+67.5 = 1067.5

I = 1000x (2.25/100) x 4 =90

1000+90 = $1090

I = 1000x (2.25/100) x 10 =225

1000+90 = $1225

Feel free to ask for more if needed or if you did not understand something.

Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

Answer:

C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.

Step-by-step explanation:

If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.

The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Let's check all the options, then we have

A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.

B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.

C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.

D: The number of bacteria doubles every hour.  It is an example of the exponential function.

The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.

More about the average rate change link is given below.

https://brainly.com/question/28744270

#SPJ5

Answer:

The regression model is:

y = 20.29 + 0.73·x

Step-by-step explanation:

In this case a regression model is to be formed to predict the final average in the course based on the first test grade.

Use Excel to form the regression model.

The output is attached below.

The regression model is:

y = 20.29 + 0.73·x

Predict the final average of a students who made an 83 on the first test as follows:

y = 20.29 + 0.73·x

  = 20.29 + 0.73 × 83

  = 80.88

The final average of a students who made an 83 on the first test would be 80.88.

From the output:

R² = 0.839

Then the correlation coefficient will be:

[tex]r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92[/tex]

The value of r is 0.92.

The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).

In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.

Step-by-step explanation:

Given,

a student (Charles) bought a car and sold it in 15 % profit for $4669.

we have the formula,

[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]

so,

[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]

by simplifying it we get,

CP is $4060.

Therefore, the cp was $4060.

Hope it helps...

Answer:

Step-by-step explanation:

(3,-2)

plug in 3 for x and -2 for y

-2< -1/2x3+2

-2<-1.5+2

-2<0.5

Answer:

A. Cone

D. Rectangular Prism

E. Cylinder

F. Sphere

Step-by-step explanation:

Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.

Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.

The proportions will look as follows:

(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)

-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.

In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.

Let's start with problem a, to show how this works:

Triangle 1 side lengths - 16, a, 11

Triangle 2 side lengths - 8, 3, b

As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.

a / 3 = 16 / 8

48 = 8a

a = 6

Next, let's find the length of side b on triangle 2.

11 / b = 16 / 8

16b = 88

b = 5.5

Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.

Triangle 1 side lengths: 5, 5.5, d

Triangle 2 side lengths: 15, c, 18

5 / 15 = 5.5 / c

5c = 82.5

c = 16.5

5 / 15 = d / 18

15d = 90

d = 6

Hope this helps!! :)

Answer:

On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.

On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.

Step-by-step explanation:

Hope this helped

Answer: Probability of visiting at most twice = 0.82

Step-by-step explanation: The probability distribution is of the form:

 X      0         1           2            3

P(X)  0.17   0.33      0.32       0.18

It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).

Using the "OR" probability:

P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)

P(visiting at most twice) = 0.17 + 0.33 + 0.32

P(visiting at most twice) = 0.82

Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

[tex] a^n = a ( n-1 ) * r [/tex]

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

Third term: a³ = 15 * ½ = 7.5

Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

Answer:  see below

Step-by-step explanation:

1) Foci is plural for Focus.  Since a hyperbola has two focus points, they are referred to as foci.  The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

    a)  does the hyperbola open up or to the right?

    b)  what is the center (h, k) of the hyperbola?

    c)  What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]

Answer:

No solutions

Step-by-step explanation:

14(z + 3) = 14z + 21

Expand brackets.

14z + 42 = 14z + 21

Subtract 14z on both sides.

42 = 21

There are no solutions.

Answer:

No solution

Step-by-step explanation:

First, We have to simplify the right side.

Distribute 14, 14z+42.

Now the equation stands as 14z+42=14z+21

Subtract 14z from both sides,

this makes it 42=21.

We know when the solution is #=#, our answer is no solution.

Answer:  6 feet from the pivot point

Step-by-step explanation:

Girl's weight x distance from center = Boy's weight x distance from center

65 (7) = 75x

[tex]\dfrac{65(7)}{75}=x[/tex]

6.066 = x

The boy needs to be placed 6 feet from the center (aka pivot point) which is the same as saying 1 foot from the end of the seesaw.

Answer:

3s-4bbb=17

Step-by-step explanation:

brother=4bbb

sister=3s

3s-4bbb=17

Answer:

<4 is congruent to angle <6

Step-by-step explanation:

Assuming the lines are parallel

<2 , <4 , <6 , <8 are all equal

Congruent means they are equal.

There are 3 angles that are the same as angle 6, they are 2, 4, 8

The answer would be B. angle 4

Answer:  4:9

Step-by-step explanation:

The complete question is provide in the attachment below.

Given, Number of females = 125

Number of males = 100

Total people = 120+100=225

Now, the ratio of males to the total number of people present = [tex]\dfrac{\text{Total number of males}}{\text{Total people}}[/tex]

[tex]=\dfrac{100}{225}[/tex]

Divide numerator and denominator by 25 , we get

Ratio of males to the total number of people present =[tex]\dfrac{4}{9}[/tex]

Hence, the ratio of males to the total number of people present =  4:9