Sam is proving the product property of logarithms.

Answer:

8 inches

Step-by-step explanation:

Let w represent the width.

If the length is 14 inches longer than the width, it can be represented by w + 14.

Use the perimeter formula, p = 2l + 2w. Plug in 60 as the perimeter and w + 14 as l, then solve for w:

p = 2l + 2w

60 = 2(w + 14) + 2w

60 = 2w + 28 + 2w

60 = 4w + 28

32 = 4w

8 = w

So, the width is 8 inches

Answer:

1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } \approx 1.665[/tex]

2) [tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]

3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } \approx 1.317[/tex]

Step-by-step explanation:

1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} }[/tex]

This integral can be solved easily by using algebraic substitutions:

[tex]u = \ln x[/tex], [tex]du = \frac{dx}{x}[/tex]

Then, the integral can rewritten as follows:

[tex]\int {\frac{dx}{2\cdot x\cdot \sqrt{\ln x}} } = \frac{1}{2}\int {\frac{du}{u^{1/2}} } = \frac{1}{2}\int {u^{-1/2}} \, du[/tex]

[tex]\int {u^{-1/2}} \, du = 2\cdot u^{1/2} + C = 2\cdot \sqrt{\ln x} + C[/tex]

Where [tex]C[/tex] is the integration constant.

[tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } = F(16) - F(2)[/tex]

[tex]F(16) - F(2) = 2\cdot (\sqrt{\ln 16}-\sqrt{\ln 2})[/tex]

[tex]F(16) - F(2) \approx 1.665[/tex]

2) Let be [tex]y = \cosh^{-1} (2\cdot \sqrt{x+1})[/tex], then we obtain the expression by the definition of the derivative for the inverse hyperbolic cosine and the chain rule:

[tex]\frac{dy}{dx} = \pm\frac{1}{\sqrt{4\cdot x + 3}}\cdot \left(\frac{1}{\sqrt{x+1}} \right)[/tex]

[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{(4\cdot x + 3)\cdot (x+1)}}[/tex]

[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]

3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} }[/tex]

This integral can be solved by the following trigonometric substitutions:

[tex]\frac{2}{\sqrt{4 + x^{2}}} = \cos \theta[/tex]

[tex]\frac{1}{\sqrt{4+x^{2}}} = \frac{\cos \theta}{2}[/tex]

[tex]\frac{x}{2} = \tan \theta[/tex]

[tex]x = 2\cdot \tan \theta[/tex]

[tex]dx = 2\cdot \sec^{2}\theta \,d \theta[/tex]

[tex]\int {\frac{dx}{\sqrt{4+x^{2}}} } = \int {\left(\frac{\cos \theta}{2} \right)\cdot (2\cdot \sec^{2}\theta)} \, d\theta = \int {\sec \theta} \, d\theta[/tex]

[tex]\int {\sec \theta}\,d\theta = \ln |\sec \theta + \tan \theta| + C[/tex]

[tex]\ln \left|\frac{\sqrt{4+x^{2}}}{2} + \frac{x}{2} \right| + C[/tex]

Where [tex]C[/tex] is the integration constant.

[tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } = F(2\sqrt{3}) - F(0)[/tex]

[tex]F(2\sqrt{3}) - F(0) = \ln \left|2+\sqrt{3}\right|-\ln \left|1\right|[/tex]

[tex]F(2\sqrt{3}) - F(0) \approx 1.317[/tex]

Answer:

7=x

Step-by-step explanation:

6(x-3)=8(x-4)

Distribute

6x -18 = 8x-32

Subtract 6x from each side

6x-18 -6x = 8x-32-8x

-18 = 2x-32

Add 32 to each side

-18+32 = 2x-32+32

14 = 2x

Divide by 2

14/2 =2x/2

7=x

[tex]\sf\purple{x= 7}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex]➺\:6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6x - 18 = 8x - 32[/tex]

[tex]➺ \: 6x - 8x = - 32 + 18[/tex]

[tex]➺ \: - 2x = - 14[/tex]

[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]

[tex]➺ \: x = 7[/tex]

Therefore, the value of [tex]x[/tex] is 7.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]

[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]

[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]

[tex]➺ \: 24 = 24[/tex]

➺ L. H. S. = R. H. S.

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:  30 boys

Step-by-step explanation:

Boys:Girls

3       : 1

Let no. of girls =x

⇒ no. of boys =3x.

⇒ no. of students in class =4x

                                            =   4/3×3x

                                            =  4 /3  ×no. of boys

  40=4/3* no.of boys

40* (3/4)=no.of boys

30=no of boys

Answer:

D

none

Step-by-step explanation:

-3,-14,-25,-36

a=-3

d=(-14-(-3))=-14+3=-11

[tex]g_{n}=a+(n-1)d\\g_{n}=-3+(n-1)(-11)\\g_{n}=-3-11n+11\\g_{n}=8-11n[/tex]

so none of them is correct.

g(1)=8-11(1)=-3

which is correct.

Answer:

we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm

The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8

The function is given as:

[tex]f(x) = -2x + 8[/tex]

The above function is a linear function.

A linear function is represented as:

[tex]y =mx + c[/tex]

Where:

m represents the slope, and c represents the y-intercept.

So, by comparison;

[tex]m =-2[/tex]

[tex]c = 8[/tex]

This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8

See attachment for the graph of the function

Read more about linear functions at:

https://brainly.com/question/15602982

Answer:

f(x) =3 (5) ^x +5

Step-by-step explanation:

f(x) = g(x) +5

We know g(x) = 3 (5) ^x

Substitute this into f(x)

f(x) =3 (5) ^x +5

Answer:

[tex] \small \sf \: f(x) = 3(5) {}^{x} + 5[/tex]

[tex] \small \sf \mapsto \: f(x) = 3(5) {}^{x} \: + 5[/tex]

Where, we have given

[tex] \small \sf \mapsto \: g(x) = 3(5) {}^{x} [/tex]

put the value of g ( x )

[tex] \small \sf \mapsto \: f(x) = 3(5) {}^{x} + 5[/tex]

Answer:

The measures of the angles are 85 and 95 degrees each.

Step-by-step explanation:

Two angles are supplementary when they add up to 180 degrees.

Therefore, set up an equation and solve for the variable x in the first place.

(8x-3)+(7x+18)=180

8x-3+7x+18=180

8x+7x-3+18=180

15x-3+18=180

15x+15=180

15x=165

x=165/15

x=11

Angle 8x-3=8(11)-3=88-3=85.

Angle 7x+18=7(11)+18=77+18=95.

Answer:

85⁰ and 95⁰

Step-by-step explanation:

Supplementary angle add up to 180⁰

8x-3+7x+18=180

8x+7x-3+18=180

15x+15=180

15x=180-15

15x=165

15x/15=165/15

x=165/15

x=11⁰

measure of first angle=8(11⁰)-3

=88⁰-3

=85⁰

measure of second angle=7(11⁰)+18

=77⁰+18

=95⁰

Answer:

Cost = 11 + 4*t

Step-by-step explanation:

Cost = 11 + 4*t

Part A

t = 5 hours.

Cost = 11 + 4*5

Cost = 11 + 20

Cost = 31

Part B

time = t hours.

Cost = 11 + 4*t

for 5h he would need to pay $20 ( +$11 ) $31

i dont know what T is so ya :/

Answer:

16 (sixteen) is 6 divided by 3/8.

Answer:

The motor oil retailer needs 15 gallons of oil, so he will have to use both tanks, and still have 1 gallon of oil short.

Step-by-step explanation:

Since a motor oil retailer needs to fill 60 one quart bottles, and he has two tanks: one that contains 12 gallons of oil and one that contains 2 gallons of oil, to determine which will need to fill the bottles, the following calculation must be performed:

Quart to gallon = 4: 1

1/4 x 60 = X

60/4 = X

15 = X

Therefore, the motor oil retailer needs 15 gallons of oil, so he will have to use both tanks, and still have 1 gallon of oil short.

Answer:

[tex]36\pi {a}^{3} [/tex]

Step-by-step explanation:

Volume = [tex] \frac{4}{3} \times \pi \times (r)^{3} [/tex]

[tex] \frac{4}{3} \times \pi \times {3a}^{3} [/tex]

[tex] \frac{4\pi}{3} \times {3}^{3} [/tex]

[tex] \frac{4\pi}{3} \times 27[/tex]

[tex] \frac{4\pi}{3} \times (3(9))[/tex]

[tex]4\pi \times 9[/tex]

[tex]36\pi {a}^{3} [/tex]

Answer:

No

Explanation:

The independent irrelevant alternative criterion is not violated here. The law of irrelevant alternative criterion holds that if candidate A is liked more than candidate B then a new candidate C who is liked less than candidate A should not spoil the victory of Candidate A, so that candidate B wins.

In the example in the question, candidate Parker was the preferred candidate before the elimination of candidate Myers and so will still be the winner of the election, therefore the irrelevant alternative criterion has not been violated.

Answer:

pls give me brainliest plzzzzz

Answer:

C D E

Step-by-step explanation:

They are the options that are clear enough

Answer: required value of c = 79.94.

Step-by-step explanation:

Let x denotes the exam score.

Given: The mean score is 76 and the standard deviation is 11.

to detrmine c , such that the probability of a student having a score greater than c  is 36 %.

or P(x>c)=0.36

Using z-score table , we get

z= 0.3584 [z-value corresponds to p-value of 0.36(one-tailed) is 0.3584]

Formula for z:

[tex]z=\dfrac{x-mean}{standard\ deviation}\\\\ 0.3584=\dfrac{c-76}{11}\\\\ c=0.3584\times11+76\\\\ c=76+3.9424\\\\ c\approx 79.94[/tex]

hence, required value of c = 79.94.

Answer:

19

Step-by-step explanation:

Answer:

i think the answer 17

Answer: The height of the triangle is 23.3 cm

Step-by-step explanation:

To calculate the area of a triangle, we use the equation:

[tex]Area=\frac{1}{2}\times b\times h[/tex]

where,

b = base of the triangle = 3 cm

h = height of the triangle = ?

Area of the triangle = [tex]35cm^2[/tex]

Putting values in above equation, we get:

[tex]35cm^2=\frac{1}{2}\times 3cm\times h\\\\h=\frac{2\times 35}{1\times 3}=23.3cm[/tex]

Hence, the height of the triangle is 23.3 cm

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

Explanation:

The two angles that involve x are alternate interior angles.

Due to the parallel lines, the alternate interior angles are equal.

We'll use this to solve for x

-7x-18 = -9x-46

-7x+9x = -46+18

2x = -28

x = -28/2

x = -14

Let's check the answer by evaluating each expression as shown below

Both angles are 80 degrees each, so it confirms we have the correct x value.

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

We have one last step. We found the -9x-46 angle to be 80 degrees. Angle 4 is adjacent to this and supplementary.

So we subtract from 180 to get the answer

180-80 = 100

Null hypothesis: [tex]p = 0.81[/tex]

Alternative hypothesis: [tex]p \ne 0.81[/tex]

The null is based on a recent study that 81% of the population (in this case senior citizens) takes at least one medication. The alternative hypothesis is basically the flip of the claim made in the null.

If Amelia wanted to know if the percentage was less than 81%, then the alternative would be p < 0.81

If Amelia wanted to know if the percentage was larger than 81%, then the alternative would be p > 0.81

However, she wants to know if the percentage is 81%.

If Amelia needed to know if the percentage was less than 81 percent, she could use p < 0.81 as an alternative and if the percentage was larger than 81 percent, she could use p > 0.81 as an alternative.

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

A recent study suggested that 81% of senior citizens take at least one prescription medication.

Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital.

She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication.

The null and alternative hypotheses for this hypothesis test will be

Null hypotheses

p = 0.81

Alternative hypotheses

p ≠ 81

According to a recent study, 81 percent of the population (in this case elderly folks) uses at least one drug. The alternate hypothesis is essentially the inverse of the null hypothesis.

If Amelia needed to know if the percentage was less than 81 percent, she could use p < 0.81 as an alternative.

If Amelia needed to know if the percentage was larger than 81 percent, she could use p > 0.81 as an alternative.

More about the null hypotheses and alternative hypotheses link is given below.

https://brainly.com/question/9504281

Answer:

i don't have any paper by me but it would be the line starting on 2 on the Y axis (line that goes up and down) and then going diagonal by one square (essentially up one unit and right one unit)

Step-by-step explanation:

2+x is basically x+2

since x is by itself in slope form is represents 1/1 as a fraction, and in slope form 2 represents the Y axis

did my best to explain sorry hope this helped!!

Step-by-step explanation:

answer is in photo above

Answer:

14

Step-by-step explanation:

take 312 + 12×14 then take 36×14

Answer:

750 profit

Step-by-step explanation:

Given :

Profit of 10 on white cement

Loss of 5 on Grey cement

Number of white cement sold = 325 bags

Number of Grey cement sold = 500 bags

Total profit made on sale of white cement :

10 * 325 = 3250

Loss made on sale of Grey cement :

5 * 500 = 2500

Total profit or loss :

3250 - 2500

= 750

Profit value is greater than. Loss value (hence, total profit of 750 was made).

Answer:

Espera espera espera.......

primer miembro es el independiente

incógnitas es la letra literal x b y c m

coeficiente es el resultado de la división

terminos independientes son aquellos los que no tienen cualquier letra 18 16 8

Step-by-step explanation:

espero que ayude

Answer:

The height of the building is of 48.24 feet.

Step-by-step explanation:

Height after t seconds:

The height after t seconds of the coin is given by:

[tex]S(t) = -16t^2 + 2t + h[/tex]

In which h is the height of the building.

If the coin hit the ground in exactly 1.8 seconds, how high is the building?

This means that when [tex]t = 1.8, S(t) = 0[/tex]. We use this to find h.

[tex]S(t) = -16t^2 + 2t + h[/tex]

[tex]h = 16t^2 - 2t[/tex]

[tex]h = 16(1.8)^2 - 2(1.8)[/tex]

[tex]h = 48.24[/tex]

The height of the building is of 48.24 feet.

Answer:

a) The number of students who enjoy reading only.

Answer:

d

Step-by-step explanation

let me know if this is right please