A woman wishes to rent a house within 9 miles of her work. If she lives x miles from her work, her transportation cost will be cx dollars per year, while her rent will be 49c x 1 dollars per year, where c is a constant taking various situational factors into account. How far should she live from work to minimize her combined expenses for rent and transportation

After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.

Using the given exponential growth model, we have:

\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)

Therefore, the population of the rural city in 2030 is approximately 11,014.18.

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Answer:

Slope undefined (vertical line)

Step-by-step explanation:

m = (y-y)/(x-x)

(50-15)/(20-20)

35/0

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Answer:

164m (to 3 s.f.)

Step-by-step explanation:

Please see the attached picture for the full solution.

The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

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Answer:

Merton will have about 6,000 more people than Hapville

Step-by-step explanation:

Merton

y = 12,000(1.04)^(30)

y = 12,000(3.24339)

y = 38,920.77012

Hapeville

y = 18,000 + (30 x 500)

y= 18,000 + 15,000

y = 33, 000

Merton - Hapeville

38,920.77012 - 33,000 = 5920.77012

Therefore Merton will have about 6,000 more people than Hapville

Answer:

9.50$

Step-by-step explanation:

First, multiply 20 by the given fractions

20*1/8=2.5

20*2/5=8

Add the two together to get the total amount of money Jeff spent, 10.5, then subtract 10.5 from 20 to get the total amount he has left, 9.5

Answer:

$9.50

I did a test with this question and the correct answer was 9.50

About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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the anwenser is 3.5 hope this helped :}

Answer:

3.5

Step-by-step explanation:

the answer is 3.5, not 5 don't let the "calculator" trick you

Answer:

1.5 feet

Step-by-step explanation:

V = base area x height

divide the two members by the base area

height = V/ base area

height = 13.5 / 9 = 1.5 feet

Answer:

145 m/s

Step-by-step explanation:

v = u + 2at

v = 19 + 2(3)(21)

v = 19 + 126

v = 145

answer

V=145

Step-by-step explanation:

V=U+2at

v=19+2×3×21

v=19+126

v=145

Answer:

He needs to add approximately $ 426.63 to his account to reach the desired balance of  $7000.

Step-by-step explanation:

Here, the principal amount, P = $ 3000,

Semiannual rate of interest, r = 8 %

Time, t = 10 years,

Hence, the amount after 10 years, which is compounded with the semiannual rate of 8% for 10 years,

Thus, the amount, need to add in the balance to reach the amount of $ 7000 = 7000 - 6573.3694291 = 426.6305709 ≈ $ 426.63

⇒ He needs to add approximately $ 426.63 to his account to reach the desired balance of  $7000

The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.

It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Fractions simply means, numbers that are not whole.

If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

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Answer:

When the denominator of a fraction is equal to 1 and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Step-by-step explanation:

I took a 2.12 math quiz in K12 and got it 100% Correct! Yes!

Answer:

I'm pretty sure the answer is 21/20 or 1.05

What is 7 1/5 written as a percent?

720%

We know that 1/5 is the same as dividing 1 by 5.

or 1÷5.

Therefore, \(7\frac{1}{5}\) \(= 7+ (1/5)\)

Then using  Long Division for 1 divided by 5  we have

7 + 0.2 = 7.2

Converting our number to a percentage:

7.2(100)

= 720%

Therefore, 7 1/5 as a percent is 720%

If you need more help, don't fret to message me!

I'll be glad to assist.

Subject: Mathematics

Concept: Conversions

Grade: Middle/High

Answer:

6th of June. I have to be the same.

Answer:

There are 60 seconds in a minute and 60 minutes in an hour so in 1,000,000 seconds there are 1,000,000/60 60 = 277.76 hours in one million seconds.

Answer:

t=-4

Step-by-step explanation:

t+6=7/3.5

t+6=70/35 (I expanded 7/3.5 by multiplying both numerator and the denominator by 10)

t+6=2 (I divided 70 by 35 to get 2)

t=2-6

t=-4

Answer:

t=-4

Step-by-step explanation:

i took the test on k12

Answer:

303 miles per hour

Step-by-step explanation:

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

1. The critical value to be used for constructing the confidence interval is 1.415

2. The standard error of the sampling distribution to be used in constructing the confidence interval, is approximately 6.260

Step-by-step explanation:

The number of mail-order receipts, n₁ = 8 sales receipts

The mean amount of sale, \(\bar x_1\) = $69.30

The standard deviation of the sample, σ₁ = $26.25

The number of internet sales receipts, n₂ = 17 sales receipts

The mean amount of sale, \(\bar x_2\) = $75.90

The standard deviation of the sample, σ₂ = $28.25

1. Where the population variance are not equal, we have;

\(\left (\bar{x}_1-\bar{x}_{2} \right ) - t_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}< \mu _{1}-\mu _{2}< \left (\bar{x}_1-\bar{x}_{2} \right ) + t_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}\)

Where;

\(t_c\) = The critical value for constructing the confidence interval

\(\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}\) = \(S.E_{\bar{x}_1-\bar{x}_{2}} =\) The standard error for constructing the confidence interval

The degrees of freedom, df = n₁ - 1 = 8 - 1 = 7

The t-value at 90% confidence level, and degrees of freedom of 7, \(t_{90\%, 7}\), from the tables is given as follows;

\(t_c\) = \(t_{90\%, \, 7}\) = 1.415

The critical value for constructing the confidence interval = \(t_c\) = 1.415

2. The standard error of the sampling distribution to be used in constructing the confidence interval, \(S.E._{\bar{x}_1-\bar{x}_{2}}\), is given as follows

\(S.E_{\bar{x}_1-\bar{x}_{2}} = \sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}\)

\(S.E._{\bar{x}_1-\bar{x}_{2}} = \sqrt{\dfrac{26.25^{2}}{8}-\dfrac{28.25^{2}}{17}} \approx 6.260\)

\(S.E._{\bar{x}_1-\bar{x}_{2}}\) ≈ 6.260

The standard error of the sampling distribution to be used in constructing the confidence interval, \(S.E._{\bar{x}_1-\bar{x}_{2}}\) ≈ 6.260

16 is the number which is one-fifth of a number when one-fourth of that same number is 20.

As per the given data:

One-fourth of the number is resulted to 20.

Here we have to determine the result of one-fifth of the same number from the given options.

An expression for a portion of a whole is a fraction.

For any real numbers, the fractional component of x is defined.

Let the number be X.

One-fourth of a number is 20 which means:

Multiply the one-fourth fraction with an unknown number which results in the number 20.

\($\frac{1}{4}\)  (X) = 20

X = 20 × 4

X = 80

Now we have to determine that one-fifth of the same number.

Multiply the one-fifth fraction by 80.

We get:

= \($\frac{1}{5}\) (80)

= \($\frac{1}{5}\)   × 5 × 16

= 16

One-fifth of the number 80 is 16

Therefore Option (D) - 16 is the correct answer.

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Answer:

the greatest common factor of 4y' and

and 11y4. is y

Answer: These are non- consistent and can be solved. The signs of the y terms are the opposite.

Step-by-step explanation: If the signs are the same, and all the terms of one equation are multiples of the other, they are identies, with infinite solutions. We can solve this system by multiplying the first equation by 2, adding the equations to cancel the y terms, and solve for x.

2(3x+y=5) becomes

6x +2y= 10 Add it to the other equation

6x -2y= 10 We are left with

12x = 20 Solve for x

x = 5/3 Substitute for x and solve for y.

3(5/3) + y = 5

5 + y = 5. Subtract 5 from both sides.

y = 0

The solution to this system is (5/3 , 0)

Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.

What are trigonometric functions?

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the angle a ladder makes with the ground should be no greater than 67°.

So the angle θ ≤ 67°.

Let us assume the angle to be equal to 67°

The height of the roof from the ground is 23 feet.

The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.

With the sine function, find the length of the ladder -

sin θ = perpendicular/hypotenuse

Let the length of ladder be x.

sin 67° = 23/x

x = 23/sin 67°

x = 23/0.920

x = 25 feet

Therefore, the length of the ladder is 25 feet.

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Answer: 700 Hamburgers

Answer:

I believe the answer is 700

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer:

\(0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570\)

\(0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630\)

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

\( n = 1019\) represent the sampel size

\( \hat p=0.6\) represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by \(\alpha=1-0.95=0.05\) and \(\alpha/2 =0.025\). And the critical value would be given by:

\(z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96\)

The confidence interval for the mean is given by the following formula:  

\(\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\)

Replacing the info given we got:

\(0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570\)

\(0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630\)

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Answer and Step-by-step explanation:

The Word form is:

Six hundred, seventy-two thousand, eight hundred and twenty nine.

The Expanded form is:

600,000 + 70,000 + 2,000 + 800 + 20 + 9

The Unit form is:

6 one hundred thousands, 7 ten thousands, 2 thousands, 8 hundreds, 2 tens and 9 ones.

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