Factor the following.

Answer:

x = -5 is your answer

Step-by-step explanation:

option c

We are given the functions:

S (p) = 40 + 0.008 p^3                                     ---> 1

D (p) = 200 – 0.16 p^2                                     ---> 2

T o find for the price in which the price of supply equals demand, all we have to do is to equate the two equations, equation 1 and 2, and calculate for the value of p, therefore:

S (p) = D (p)

40 + 0.008 p^3 = 200 – 0.16 p^2

0.008 p^3 + 0.16 p^2 = 160

p^3 + 20 p^2 = 20,000

p^3 + 20 p^2 – 20,000 = 0

Calculating for the roots using the calculator gives us:

p = 21.86, -20.93±21.84i

Since price cannot be imaginary therefore:

p = 21.86

Answer:

15 mph

Step-by-step explanation:

Speed of wind = [tex]V_w[/tex] = 4 mph

Speed of Jaime rowing = [tex]V_r[/tex]

Speed of boat against wind = [tex]V_r-4[/tex].

Speed of boat with wind = [tex]V_r+4[/tex]

Time taken with and against wind is same = t

Distance travelled with wind = 57 mph

Distance travelled against wind = 33 mph

[tex]time=\frac{\text{Distance}}{\text{Speed}}[/tex]

Time taken to go with wind

[tex]t=\frac{57}{V_r+4}[/tex]

Time taken to go against wind

[tex]t=\frac{33}{V_r-4}[/tex]

So,

[tex]t=\frac{57}{V_r+4}=\frac{33}{V_r-4}\\\Rightarrow \frac{57}{33}=\frac{V_r+4}{V_r-4}\\\Rightarrow 57V_r-33V_r-228-132=0\\\Rightarrow V_r=\frac{360}{24}\\\Rightarrow V_r=15\ mph[/tex]

∴ Her normal rowing speed with no wind is 15 mph

The balance in your account after five years will be approximately $1,118.85.

Step 1: Understand Continuous Compounding

In continuous compounding, interest is earned not only on the initial principal amount but also on the accumulated interest over time. This means interest is calculated continuously throughout the year, leading to a slightly higher final balance compared to simple interest.

Step 2: Formula for Continuous Compounding

The formula for continuous compounding to find the future value (balance) after t years is:

A = P * e^(r*t)

where:

Step 3: Apply the Formula

Step 4: Calculate the Final Balance

You can use a calculator to evaluate the expression.

A ≈ $750 * e^(0.4) ≈ $750 * 1.4918

Step 5: Round the Answer (Optional)

Depending on the desired level of precision, you can round the answer to two decimal places:

A ≈ $1118.85 (rounded to two decimal places)

We cannot definitively conclude the sprinter's improvement in time due to the ±0.05 seconds uncertainty of the stopwatch. Additionally, the stopwatch's uncertainty hinders accurate timing in close races, making it possibly unhelpful for precise measurements.

The subject of the question is probability, but the scenario provided deals with the uncertainty of a stopwatch rather than the probabilities of breaking records. The uncertainty of the stopwatch is ±0.05 seconds. Analyzing the times recorded, the sprinter's time improved from 12.04 seconds to 11.96 seconds, but due to the stopwatch's uncertainty, it's not possible to definitively conclude that this week's time was faster since both times could vary by ±0.05 seconds. Likewise, when the times of the first and second place sprinters at the last track meet are considered, the difference in their times is 0.03 seconds, which is within the margin of error of the stopwatch. Therefore, the new stopwatch might not be helpful in accurately determining the winner in close races where the time difference is within the uncertainty range of the stopwatch.

To determine how long it will take for the jet to catch up to the airplane, calculate the time by dividing the distance the airplane covers before the jet starts (180 miles) by the relative speed of the jet to the airplane (150 mph), resulting in 1.2 hours or 72 minutes.

The subject of the question is related to the topic of relative velocity in Mathematics, specifically regarding two objects moving in the same direction. To find out how long it will take for the jet to catch up to the airplane, we need to calculate the relative speed of the two vehicles and the time it takes for one to overtake the other.

The airplane is moving at 180 mph, and the jet is flying at 330 mph. Since the jet leaves one hour later, the airplane would have traveled 180 miles by that time. The relative speed of the jet to the airplane is the difference between their speeds, which is 330 mph - 180 mph, resulting in 150 mph.

To catch up, the jet needs to cover the 180 miles separation distance at a relative speed of 150 mph. We can find the time it takes to catch up by dividing the distance by the relative speed:

Time = Distance ∗ Relative Speed = 180 miles ∗ 150 mph = 1.2 hours.

Therefore, it will take 1.2 hours or 72 minutes for the jet to catch up to the airplane after it starts its pursuit.

Answer:

  x = 16

Step-by-step explanation:

Add 1.2 to both sides, then divide by the coefficient of x.

  3.7x = 59.2

  x = 59.2/3.7 = 16

The value of x is 16.

Secants from the same point have the same product of length to the near intersection times length to the far intersection from the point.

1) 5(5+x) = 6(6+4)

... 25 + 5x = 60 . . . . eliminate parentheses using the distributive property

... 5x = 35 . . . . . . . . subtract 25

... x = 7 . . . . . . . . . . . divide by 5

2) The same rule applies.

... 3(3+5) = 4(4+x)

... 24 = 16 + 4x . . . . . eliminate parentheses

... 8 = 4x . . . . . . . . . . . subtract 16

... 2 = x . . . . . . . . . . . . divide by 4

The sum of x and y that cannot be obtained from the equation 3x + y = 14 is 8.

The question asks for the sum of x and y that could not be obtained from the equation 3x + y = 14. To find the possible values of x and y, we need to consider different combinations of positive integers that satisfy the equation. If we test the answer choices, we can see that the sum of x and y cannot be equal to 8. Therefore, the correct answer is C) 8.

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the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5 is 716144

Given that,
What is the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5 is to be determined.

Arithmetic progression is the series of numbers that have common differences between adjacent

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

the formula of the sum of the 1st nth term in a Geometric Progression:

[tex]Sum = a_1(1-r^n)/(1-r) \\Sum = -11(1 - (-5)^8)/(1+5)\\sum = -11(1 - 390625)(6)\\Sum = 716144[/tex]

Thus, the required sum of the 8-term geometric series is 716,144.

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The dimensions of her rectangular flower bed will be 4 feet by 6 feet.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

Geneva needs to put fencing around her rectangular bloom bed. The width of her bloom bed is 2/3 the length.

W = (2/3)L

3W = 2L

The perimeter of the bloom bed is 20 feet. Then we have

2(L + W) = 20

2L + 2W = 20

3W + 2W = 20

5W = 20

W = 4 feet

Then the length of the rectangle is given as,

2L = 3 x 4

L = 6 feet

The dimensions of her rectangular flower bed will be 4 feet by 6 feet.

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Answer:

n = [tex]3\frac{1}{4}[/tex] and m = [tex]2\pi[/tex]

Step-by-step explanation:

From the given figure we have,

'n' belongs to rational numbers but it is not an integer.

'm' belongs to irrational numbers.

Now, we look at the options,

a) n = [tex]\frac{1}{3}[/tex] , m = [tex]\sqrt{4}[/tex] = 2 is wrong as m is not a rational.

b) n = [tex]3\frac{1}{4}[/tex] and m = [tex]2\pi[/tex] is correct

c) m = [tex]\sqrt{3}[/tex] , n = [tex]\frac{4}{2}[/tex] = 2 is wrong as n is not an integer

d) m = [tex]\frac{\pi }{2}[/tex] , n = [tex]\sqrt{6}[/tex] is wrong as n is not an irrational number.

The two possible values of n and m are ; n = 3¼ and m = 2π

From the rules given;

Evaluating the numbers given ; rational numbers can be whole numbers or fractions which can be expressed in form a/b where b ≠0.

All π values are irrational .

From the option, the value pairs which meets the requirements are ;

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Final answer:

To take the square root of a number, use the square root function on a calculator or raise the number to the power of 0.5. For higher roots, like fourth roots, raise to the power of 0.25, or take the square root twice. Adjust exponentials before taking roots and estimate if a calculator is not available.

Explanation:

To take the square root of a number, you can perform this operation either by using a calculator or through manual calculations. If you're using a calculator, simply use the square root function, which is usually represented by a radical sign (√) or sometimes as a button labeled 'sqrt'. However, when dealing with equations or expressions where the variable is raised to a power, such as , you will need to take the fourth root to solve for T. This is equivalent to raising the number to the 0.25 power (since 1/4 is equivalent to the fourth root). You can verify this method by checking that the square root of a number is the same as that number raised to the 0.5 power.

In case you are working with exponentials, remember to adjust the exponent so it's evenly divisible by 2 before extracting the square root. If the number is written in scientific notation, extract the square root of the coefficient and halve the exponent. For example, taking the square root of 1 x 104 would be 1 x 102 since the square root of 1 is 1 and half of 4 is 2.

When you lack a calculator, estimating roots, such as cube roots or higher, can be done with a rough mental approximation. For instance, to find the cube root of 87, you know that the cube root of 64 (which is 4) is too small and the cube root of 125 (which is 5) is too big, so you can start by guessing around 4.3. With trial, error, and adjustments, you can find a more accurate result.

Answer:  The correct option is (C) [tex]\log_242.[/tex]

Step-by-step explanation:  We are given to express the following logarithmic expression as a single logarithm :

[tex]E=\log_26+\log_27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(I)[/tex]

We will be using the following logarithmic property :

[tex]\log_ab+\log_ac=\log_a(bc)[/tex]

So, from expression (i), we get

[tex]E=\log_26+\log_7=\log_2(6\times 7)=\log_242.[/tex]

Thus, the required single logarithm is [tex]\log_242.[/tex]

Option (C) is CORRECT.

11.78*6 = 70.68 per day

70.68*7 = 494.76 per week

The probability that Aly won't purchase either car A or car B is 0.18. This is calculated by subtracting the combined probability of purchasing either car from 1.

The question pertains to the concept of probability, which can be defined as a measure of the likelihood that a given event will occur. In this case, Aly is deciding between two cars to purchase (Car A and Car B). The probability that she will purchase car A is 0.47 and the probability that she will purchase car B is 0.35. These probabilities might have been estimated based on Aly's preferences, past behavior, or other relevant factors.

Since probabilities add up to 1, we can calculate the probability that Aly won't purchase either car A or car B by subtracting the sum of the probabilities of buying car A and car B from 1. So, we do 1 - (0.47 + 0.35) = 0.18. Therefore, the probability that she will not purchase either car A or car B is 0.18.

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If you look at the clock and it is exactly 2pm. you set an alarm to go off in 51 hours then 5PM is the time when alarm go off.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

Given that You look at the clock and it is exactly 2pm and set an alarm to go off in 51 hours.

We need to find at which time the alarm go off.

We know that in a clock we will have 12 hours.

For every 12 hours the PM changes to PM.

2PM-2PM=24 hours

2PM-2PM=24 hours

When we add the hours we get 48 hours still we needed three more hours to turn off the alarm

2PM-5PM=3 hours.

at 5PM it becomes 51 hours.

Hence, if you look at the clock and it is exactly 2pm. you set an alarm to go off in 51 hours then 5PM is the time when alarm go off.

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Answer:

The required equivalent form of given expression is

[tex]\sin 3x-\sin x=2\cos 2x\sin x[/tex]

Step-by-step explanation:

Given : Expression [tex]\sin 3x-\sin x[/tex]

To find : The expression is equivalent to ?

Solution :

Applying trigonometric formula,

[tex]\sin a - \sin b = 2\cos(\frac{a+b}{2})\sin(\frac{a-b}{2})[/tex]

where, a=3x and b=x

[tex]\sin 3x-\sin x=2\cos(\frac{3x+x}{2})\sin(\frac{3x-x}{2})[/tex]

[tex]\sin 3x-\sin x=2\cos(\frac{4x}{2})\sin(\frac{2x}{2})[/tex]

[tex]\sin 3x-\sin x=2\cos 2x\sin x[/tex]

Therefore, The required equivalent form of given expression is

[tex]\sin 3x-\sin x=2\cos 2x\sin x[/tex]

The expression equivalent to (sin 3x-sin x) is 2cos(2x)sin(x) and this can be determined by using the trigonometric properties.

Given :

Expression  --  (sin 3x - sin x)

The following steps can be used in order to determine the expression equivalent to (sin 3x - sin x):

Step 1 - The trigonometric properties can be used in order to determine the expression equivalent to (sin 3x - sin x).

Step 2 - Below are the properties that help to evaluate the given expression.

[tex]\rm sin \;A - sin\;B = 2cos\left(\dfrac{A+B}{2}\right) sin\left(\dfrac{A-B}{2}\right)[/tex]

Step 3 - Use the above-mentioned property in the given expression.

[tex]\rm sin \;3x - sin \; x = 2 cos\left(\dfrac{3x+x}{2}\right) sin\left(\dfrac{3x-x}{2}\right)[/tex]

[tex]\rm sin \;3x - sin \; x = 2 cos\left(\dfrac{4x}{2}\right) sin\left(\dfrac{2x}{2}\right)[/tex]

[tex]\rm sin \;3x - sin \; x = 2 cos\left(2x\right) sin\left(x\right)[/tex]

So, the expression equivalent to (sin 3x-sin x) is 2cos(2x)sin(x).

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Answer:

Option 3 - [tex]2.04\times 10^4[/tex]

Step-by-step explanation:

Given : Numbers [tex]7.2\times 10^{-6}[/tex] , [tex]3.09\times 10^3[/tex][tex]2.04\times 10^4[/tex] and [tex]5\times 10^3[/tex]

To find : Which number is largest ?

Solution :

We solve all number in standard form,

1) [tex]7.2\times 10^{-6}=\frac{72}{10}\times \frac{1}{1000000}[/tex]

[tex]7.2\times 10^{-6}=0.0000072[/tex]

2) [tex]3.09\times 10^3=\frac{309}{100}\times 1000[/tex]

[tex]3.09\times 10^3=3090[/tex]

3) [tex]2.04\times 10^4=\frac{204}{100}\times 10000[/tex]

[tex]2.04\times 10^4=20400[/tex]

4) [tex]5\times 10^3=5\times 1000[/tex]

[tex]5\times 10^3=5000[/tex]

The decimal number is the least number among all.

The five digit number is the greatest number among all.

So, 20400 is the greatest number.

Which means [tex]2.04\times 10^4[/tex] is the largest number.

Therefore, Option 3 is correct.