What is the decibel level of a dog barking with intensity 10−5 watts per square inch? Use a logarithmic model to solve.

Answer:

Remove 9 from triangle B to A

Step-by-step explanation:

Given

Three Triangles

A: 1,2,3

B: 7,8,9

C: 4,5,6

Required

Make their sum equal

First, we need to calculate the sum in each triangles;

[tex]A = 1 + 2 + 3[/tex]

[tex]A = 6[/tex]

[tex]B = 7 + 8 + 9[/tex]

[tex]B = 24[/tex]

[tex]C = 4 + 5 + 6[/tex]

[tex]C = 15[/tex]

Remove 9 from triangle B to A

[tex]A = 6 + 9[/tex]

[tex]A = 15[/tex]

[tex]B = 24 - 9[/tex]

[tex]B = 15[/tex]

At this point, we have:

[tex]A = 15[/tex]     [tex]B = 15[/tex]     [tex]C = 15[/tex]

Hence, the solution is to remove 9 from B to A

Answer: Need more info. We need to know how many minutes over the 300 minutes were used in order to calculate the correct monthly fee.

Step-by-step explanation:

Answer:

y= 75

x= 53

Step-by-step explanation:

y= 75

Vertically opposite angles

x=53

75 + 52 = 127

angles in a triangle add up to 180

180 - 127 = 53

Hope this helps!

♣ GIVEN ♣

♣ TO FIND ♣

♣ SOLUTION ♣

In the given figure y = 75° , since y and 75° are Vertically opposite angles and vertically opposite angles are equal to each other.

Now , we know that the angle sum property of a ∆ is 180°, i.e. sum of all interior angles of a triangle is equal to 180°.

So , in the given ∆ ,

=> x + y + 52° = 180° .

=> 75° + 52° + x = 180°.

=> 127° + x = 180° .

=> x = (180 - 127)°.

☞ x = 53° .

Hence ,

Answer:

D. -7

Step-by-step explanation:

Sum of three times the square of a number and -7.

If we call the number x, then the expression is:

Here - 7 is constant, x is variable, 3 is coefficient

Correct answer choice is: D. -7

Answer:

98

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

Steps to solve:

-k^2 - (3k - 6n) + 2n; k = -3, n = -5

~Substitute ans simplify

-(-3)^2 - (3(-3) - 6(-5)) + 2(-5)

3^2 - (-9 + 30) - 10

~Use PEMDAS and solve the rest

9 - 21 - 10

-13 - 10

-23

Best of Luck!

Answer:

-2

Step-by-step explanation:

-(-3)∧2-(-9+30)+10= 9+9-30+10= -2

Answer:

the expression of the information in terms of function f is:

13 = f(40)

The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.

Step-by-step explanation:

suppose G and p are the  two unknowns variables.

where;

G is measured in tons per week and:

p is measured in thousands of people.

∴

The relation between the amount of garbage produced by a city with population p can be expressed as:

G = f(p)

However;

The town of Tola has a population of 40,000 and produces 13 tons of garbage each week.

The objective is to express the information in terms of the function f.

So, if there is a population of 40,000 person in the town,

since p is measured in person per thousand and the value of garbage produced is 13 tons per week.

∴ the expression of the information in terms of function f is:

13 = f(40)

Explain the meaning of the statement f(5) = 2.

The given statement implies that

P which is measured in thousand people = 5

and the value of the garbage produced is 2.

SO , we can say that;

The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.

Answer: [tex]x^4-x^3-16x^2+16x[/tex]

Step-by-step explanation:

Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).

Given: Zeroes of polynomial : -4,0, 1, and 4.

Then Factors = [tex](x-(-4)), (x-0), (x-1) and (x-4)[/tex]   [By factor theorem ]

[tex]=(x+4), (x-0), (x-1) and (x-4)[/tex]

Multiplying these factors to get polynomial in standard form.

[tex](x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x[/tex]

Hence, B is the correct option.

Answer:

Hi

Step-by-step explanation:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

Answer:

Inequality

Step-by-step explanation:

An inequality is mathematical sentence that compares expression that are not equal.

Answer:

Step-by-step explanation:

[tex] \sf{ {x}^{2} - 4x - 21}[/tex]

Here, we have to find the two numbers that subtracts to 4 and multiplies to 21

⇒[tex] \sf{ {x}^{2} - (7 - 3)x - 21}[/tex]

⇒[tex] \sf{ {x}^{2} - 7x + 3x - 21}[/tex]

Factor out X from the expression

⇒[tex] \sf{ x(x - 7) + 3x - 21}[/tex]

Factor out 3 from the expression

⇒[tex] \sf{x(x - 7) + 3(x - 7)}[/tex]

Factor out x-7 from the expression

⇒[tex] \sf{(x - 7)(x + 3)}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\boxed{\boxed{\bold{(x - 7)(x + 3)}}}[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 4x - 21 \\ {x}^{2} - 7x + 3x - 21 \\ x(x - 7) + 3(x - 7) \\ (x - 7)(x + 3)[/tex]

Answer:

4times tall

Step-by-step explanation:

Volume of the boxes = Base area × height

Volume of the first box V1 = A1h1

Given the base of the first box to be 5cm, the base area:

A1 = 5cm×5cm = 25cm²

Volume of the first box V1 = 25h1... 1

Similarly, volume of the second box

V2 = A2h2

Given the base of the second box to be 10cm, the base area:

A2= 10cm×10cm = 100cm²

Volume of the second box

V2 = 100h2... 2

If the two boxes have the same volume, then V1 = V2

25h1 = 100h2

divide both sides by 25

25h1/25 = 100h2/25

h1 = 4h2

Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.

Answer:

4times tall

Step-by-step explanation:

Volume of the boxes = Base area × height

Volume of the first box V1 = A1h1

Given the base of the first box to be 5cm, the base area:

A1 = 5cm×5cm = 25cm²

Volume of the first box V1 = 25h1... 1

Similarly, volume of the second box

V2 = A2h2

Given the base of the second box to be 10cm, the base area:

A2= 10cm×10cm = 100cm²

Volume of the second box

V2 = 100h2... 2

If the two boxes have the same volume, then V1 = V2

25h1 = 100h2

divide both sides by 25

25h1/25 = 100h2/25

h1 = 4h2

Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.

Answer:

y-11

Step-by-step explanation:

First you divide 3 by 3 to get one. Then you add 12 to -1 to get 11. Then you will have y-11. PEMDAS saves lives.

Answer:

y = - 11

Step-by-step explanation:

Let y - 3/3 + 12 = 0

Multiply through by 3, we have as follow:

3y - 3 + 36 = 0

3y + 33 = 0

3y = - 33

y = -33/3 = -11

Answer:

0

Step-by-step explanation:

∫∫8xydA

converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.

So,

∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ

So we integrate r from 0 to 9 and θ from 0 to 2π.

∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ

= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ

= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ

= 8[6561/4]∫(cosθsinθ)dθ

= 13122∫(cosθsinθ)dθ

Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2

Substituting this we have

13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ

= 13122/2[-cos2θ]/2 from 0 to 2π

13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]

= -13122/4[cos4π - cos(0)]

= -13122/4[1 - 1]

= -13122/4 × 0

= 0

Answer:

S = y / (V - k⁴) where V ≠ k⁴

Step-by-step explanation:

y = SV - Sk⁴

y = S(V - k⁴)

S = y / (V - k⁴) where V ≠ k⁴

Answer:

66

Step-by-step explanation:

In statistics, the formula for RANGE is given as the difference between the Highest and the Lowest value.

In the above values we are given data consisting of the 7 games that Roger bowled.

155, 165, 138, 172, 127, 193 , 142.

Step 1

We arrange from the least to the highest.

127, 138, 142, 155, 165, 172, 193

Step 2

Lowest value = 127

Highest value = 193

Step 3

Range = 193 - 127

= 66

Therefore, the range of Roger's scores is 66

Answer:

[tex]x\geq -30[/tex]

Step-by-step explanation:

Work to isolate x on one side of the inequality:

[tex]3-\frac{x}{2} \leq 18\\3-18\leq \frac{x}{2} \\-15\leq \frac{x}{2}\\-30 \leq x[/tex]

Therefore the answer is all x values larger than or equal to -30

[tex]x\geq -30[/tex]

Answer:

The stock market increased 75 point: 75 or +75

Answer:

The stock market increased by 75 so your answer according to my understanding is +75 or 75.

Step-by-step explanation:

Hope it will help you :)

Answer:

4

Step-by-step explanation:

(10-x)/x=3/2

so 2*(10-x)=3x

20-2x=3x

+2x        +2x

20=5x

x=20/5

x=4

verify

(10-4)/4=3/2

6/4=3/2

TRUE

Answer: This is what i can do . i hope it helps:)

The angle between the longitude of the Galapagos Islands and that of Nauru is 90.30°+166.56°=256.86°.

We find the sum since these places have different longitude directions, but this is the major arc, and the minor arc will be 360°−256.86°=103.14°.

Angle between Galapagos Islands and 180°E/W = 180° - 90.30° = 89.70°

Angel between Nauru island and 180°E/W = 180° - 166.56° = 13.44°

Total angle between Galapagos Islands and Nauru = 89.70 ° + 13.44° = 103.14°.

Step-by-step explanation:

[tex]let \:\alpha \:be\:our\:teetah \\l = \frac{r \pi}{180 \°} \times \alpha \\\\= \frac{6400\pi}{180 \°} \times 103.14\\\\= 11520.848\\\\= 11521 km[/tex]

Answer:

A - the arrow on the right points to the point -2. the arrow on the left moves 7 places to the left to the point -9.

this is what the expression is stating: -2 - 7 = -9

Answer:

0.0075

Step-by-step explanation:

According to the given situation, the calculation of the probability that the TPMS will trigger a warning is shown below:-

The tire pressure which is 26% below the target pressure is

[tex]= 26\% \times 28[/tex]

= 7.28

Therefore, Tire pressure monitoring systems warn at below is

= 28 - 7.28

= 20.72

Now we will assume tire pressure be x

So,

[tex]P(X<20.72) = P(\frac{X-\mu}{\sigma}<\frac{20.72-28}{3} )[/tex]

After solving the above equation we will get

= [tex]P(X<20.72) = P(Z<-2.43)[/tex]

we will get

= 0.0075

Answer:

x=7

Step-by-step explanation:

took the test

The required solution of the equation is x = 7.

Given that,
Solution of the equation,
x / 3 + x / 6 = 7 / 2 is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The equation is the relationship between variables and represented as y = ax + b   is example of a polynomial equation.

Here,
x  / 3 + x / 6 = 7 / 2
Taking LCM on the left side
[2x + x] /6 = 7 / 2
3x / 6 = 7 / 2
x / 2 = 7 / 2
x = 7

Thus,  the required solution of the equation is x = 7.

Learn more about arithmetic here:

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Answer:

We conclude that there is no difference between the two classes.

Step-by-step explanation:

We are given that two statistics teachers both believe that each has a smarter class.

A summary of the class sizes, class means, and standard deviations is given below:n1 = 47, x-bar1 = 84.4, s1 = 18n2 = 50, x-bar2 = 82.9, s2 = 17

Let [tex]\mu_1[/tex] = mean age of student cars.

 [tex]\mu_2[/tex] = mean age of faculty cars.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]      {means that there is no difference in the two classes}  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]      {means that there is a difference in the two classes}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;

                         T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~  [tex]t_n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years

[tex]\bar X_2[/tex]  = sample mean age of faculty cars = 5.3 years  

[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years  

[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years  

[tex]n_1[/tex] = sample of student cars = 110  

[tex]n_2[/tex] = sample of faculty cars = 75  

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(47-1)\times 18^{2}+(50-1)\times 17^{2} }{47+50-2} }[/tex]  = 17.491

So, the test statistics =  [tex]\frac{(84.4-82.9)-(0)}{17.491 \times \sqrt{\frac{1}{47}+\frac{1}{50} } }[/tex]  ~  [tex]t_9_5[/tex]

                                     =  0.422    

The value of t-test statistics is 0.422.

Now, the P-value of the test statistics is given by;

P-value = P([tex]t_9_5[/tex] > 0.422) = From the t table it is clear that the P-value will lie somewhere between 40% and 30%.

Since the P-value of our test statistics is way more than the level of significance of 0.04, so we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.

Therefore, we conclude that there is no difference between the two classes.

Answer:

0.16%

Step-by-step explanation:

From the statement of the question;

Number of Laryngeal cancer due to smoking = 160

Population of smokers = 100,000

Hence the percentage of smokers liable to have Laryngeal cancer = 160/100000 ×100/1

=0.16%

Hence 0.16% of smokers are liable to Laryngeal cancer

Answer:

D

Step-by-step explanation:

Given

f(x) = 3x² - 24x + 10 ← factor out 3 from 3x² - 24x

     = 3(x² - 8x) + 10

Using the method of completing the square

add/ subtract ( half the coefficient of the x- term )² to x² - 8x

f(x) = 3(x² + 2(- 4)x + 16 - 16) + 10

      = 3(x - 4)² - 48 + 10

      = 3(x - 4)² - 38 ← in vertex form → D

Answer:

d

Step-by-step explanation:

Answer:

The first car used 30 gallons and the second one 20 gallons of gas during the trip.

Step-by-step explanation:

35x+40y = 1850     equation 1

x+y = 50        equation 2

x=car 1

y=car 2

Solve it

Solve using PEMDAS for the numerator and denominator.

24-11^4/24+11^4

24-14641/24+14641

-14617/14665

Best of Luck!

Answer:

A).Amount = $218250

B). Amount = $88700

Step-by-step explanation:

A) .$5000 in an account at age 23, and withdraw it 42 years

Number of years t= 42 years

Principal P = $5000

Rate r= 9%

Number of times compounded n= 42

A= p(1+r/n)^(nt)

A= 5000(1+0.09/42)^(42*42)

A= 5000(1+0.002143)^(1764)

A= 5000(1.002143)^1764

A= 5000(43.65)

A= 218250

Amount = $218250

B).waits 10 years before making the deposit, so that it stays in the account for only 32 years

Number of years t= 32 years

Principal P = $5000

Rate r= 9%

Number of times compounded n= 32

A= p(1+r/n)^(nt)

A= 5000(1+0.09/32)^(32*32)

A= A= 5000(1+0.0028125)^(1024)

A= 5000(1.0028125)^1024

A= 5000(17.74)

A= 88700

Amount = $88700

Answer:32

Step-by-step explanation:

768/24=32

The person buying the new computer will pay $120 more when choosing the rent-to-own option of paying $37 per week for 24 weeks over paying the whole cost of $768 at once.

A rent-to-own contract is a contract where the buyer pays for something as rent to the owner until the set period in the contract.

In the question, we are informed that a person decides to buy a new computer. He has two options to buy. Either he can pay the full cost of the computer = $768, or he can choose a rent-to-own option, in which he will pay $37 per week for 24 weeks.

We are asked to find the extra cost that the person will pay if he chooses the rent-to-own option, after completing all his payments.

The total amount that the person pays in the rent-to-own option = $37*24

or, the total amount that the person pays in the rent-to-own option = $888.

The actual cost of the computer = $768.

∴ Extra payment = Total Payment - Actual cost

or, Extra payment = $888 - $768 = $120.

∴ The person buying the new computer will pay $120 more when choosing the rent-to-own option of paying $37 per week for 24 weeks over paying the whole cost of $768 at once.

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