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2 years ago

Which of the following illustrates the product rule for Logarithmic equations?

Mathematics

2 answers:

Aleksandr [31]2 years ago

7 0

Try this option:
rule: logₐ(bc)=logₐb+logₐc;

according to the rule: log₂(4x)=log₂4+log₂x

answer: log₂4+log₂x

Makovka662 [10]2 years ago

3 0

We are given Logarithmic equations.

We need to find the equation which illustrates the product rule.

We know, the product rule of Logarithms is:

$log_b (mn) = log_b(m) + log_b(n)$ .

According to the product rule of Logarithms, we need to separate logs by plus sign.

In the given options only 4th option logs are separated by plus sign.

$log_2(4x) = log_2\ 4+log_2\ x$ .

<h3>Therefore, correct option is 4th option.</h3>

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Allie has two cars- a truck and a sedan. Last week, she used 3 gallons of gas in the truck and 5 gallons of gas in the sedan and

gavmur [86]

Answer:

sedan = 26 miles/gallon

truck = 17 miles/gallon

Step-by-step explanation:

try to write the text in mathematical format as a system of equations

t=truck s=sedan

$\left \{ {{3t+5s=181} \atop {7t+6s=275}} \right.$

first equation can be written as

t= (181-5s)/3

we can use it in the second equation and rewrite it as

7[(181-5s)/3]+6s = 275

7(181/3 -5/3s) + 6s = 275

1267/3 - 35/3s + 6s = 275

-35/3s + 18/3s = 275-1267/3

-35/3s + 18/3s = 825/3 - 1267/3

-35s + 18s = 825 -1267

-17s = -442 s = 442/17 = 26 sedan has an average of 26 miles/gallon

we use this value of s in the first equation

3t + 5*26=181 3t=181-130 t= 51/3 = 17 truck has an average of 17 miles/gallon

5 0

2 years ago

Twenty-five juniors from a University volunteer to allow their Math GRE test scores to be used in a study. These 25 juniors had

fgiga [73]

Let's start first by writing down the given:
σ = 100
sample mean = 450
sample size = 25

These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.

A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.

Next, we look for the standard error of the mean. This will have a formula
$error= \frac{standard deviation of population}{ \sqrt{N} }$

The standard error would just therefore be equal to
$\frac{100}{ \sqrt{25} }= \frac{100}{5} =20$

Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
$450-20(1.645)=417.1$
$450+20(1.645)=482.9$

ANSWER: 417.1<μ<482.9

8 0

2 years ago

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 10 of th

Digiron [165]

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

the line which represent the equation and c is the y-intercept

- The slope of the line m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

the linear equation between the cars' numbers and the weeks

numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ $m=\frac{175-200}{15-10}=\frac{-25}{5}=-5$

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

7 0

2 years ago

Read 2 more answers

Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.

Setler [38]

The answer is ：h^2/tanθ+wh

5 0

2 years ago

prove that ( sin theta cos theta = cot theta ) is not a trigonometric identity by producing a counterexample

user100 [1]

Answer:

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Assume θ with a value and substitute with it.

Let θ = 45°

So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2

R.H.S = cot θ = cot 45 = 1

So, L.H.S ≠ R.H.S

So, sin θ cos θ = cot θ is not a trigonometric identity.

8 0

2 years ago