Rita's water tank contains 7.8 gallons of water. Rita will begin filling her water tank at a rate of 2.1 gallons per minute.

Wendy's water tank contains 97.8 gallons of water. Wendy will begin draining her water tank at a rate of 0.9 gallon per minute.

After how many minutes will both water tanks contain the same amount of water?
A 25 min
B 30 min
C 35 min
D 75 min​

Answer:

f(x) = .05x; $5.50

Step-by-step explanation:

f(x) = .05x

f(110) = .05(110) = $5.50

The constants that have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Elimination Method

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables

Both x term and y terms, choose x terms  and apply the elimination method

The coefficient of x in the first equation is 5 and 12 in the second equation

Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together. 2 and x; 6 and x are factors because they are being multiplied together. 2 from 2x and 6 from 6x are the coefficients because they are being multiplied by the variable.

To make it the same

Prime factorization

Prime factorization is a process of writing all numbers as a product of primes.

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and the second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Eliminated x term

The constants that we have to multiply to eliminate one variable from the system are 12 and 5

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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To generate a list of product names and unit prices ranked by unit price into three categories (1, 2, 3) based on price, you can use a SQL query with the RANK() function.

The highest-priced products will be marked with a 1, the second-highest-priced products with a 2, and so on.

In SQL, you can use the RANK() function along with the ORDER BY clause to rank the products based on their unit prices. The RANK() function assigns a rank to each row in the result set based on the specified ordering criteria. Here's an example SQL query to achieve this:

In this query, products is the name of the table containing the product information. We select the product_name and unit_price columns from the table. The RANK() OVER (ORDER BY unit_price DESC) part ranks the rows based on the unit_price column in descending order, with the highest prices receiving a rank of 1.

The result of this query will include the product names, unit prices, and the assigned price ranks. You can then filter the results based on the price ranks to categorize the products into three categories (1, 2, 3) based on their price rankings.

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Answer:

5. there was a:  18% decrease.

6.  if the intial value was 285 and there was a 15 difference then the final value is 300. The change is 5.26%.

7. She has a 33.3333 % increase

8. The amount of students increased by 23.0769%

I hope this somewhat helps

The required regression equation is y=−15.9x+1081.6 and new cases for 2008 is 950.

To find the linear regression equation that represents the given set of data, we need to find the slope and y-intercept of the line of best fit.

We can use the following formulas to find the slope and y-intercept:

\($\begin{align*}\text{slope } b &= \frac{\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y})}{\sum_{i=1}^{n}(x_i - \overline{x})^2} \\text{y-intercept } a &= \overline{y} - b\overline{x}\end{align*}\)

where n is the number of data points, \($x_i$\) and \($y_i$\) are the i th values of x and y, respectively, \($\overline{x}$\) and\($\overline{y}$\) are the means of x and y, respectively.

Using the given data, we can calculate:

\(\overline{x} &= \frac{0+1+2+3}{4} = 1.5 \\overline{y} &= \frac{998+1047+1106+1084}{4} = 1058.75\)

\(\sum_{i=1}^{n}(x_i - \overline{x})(y_i - \overline{y}) &= (0-1.5)(998-1058.75) + (1-1.5)(1047-1058.75) \&\quad+ (2-1.5)(1106-1058.75) + (3-1.5)(1084-1058.75) \&= -79.5 \\sum_{i=1}^{n}(x_i - \overline{x})^2 &= (0-1.5)^2 + (1-1.5)^2 + (2-1.5)^2 + (3-1.5)^2 \&= 5 \\end{align*}\)

Therefore, the slope is:

\($\begin{align*}b &= \frac{-79.5}{5} \&= -15.9 \\end{align*}\)

The y-intercept is:

\(\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)\($\begin{align*}a &= 1058.75 - (-15.9)(1.5) \&= 1081.55 \\end{align*}\)

So the linear regression equation is:

y=−15.9x+1081.6

To find the projected number of new cases for 2008 (which is 8 years after 2000), we substitute x=8 into the equation and round to the nearest whole number:

\($\begin{align*}y &= -15.9(8) + 1081.6 \&= 949.8 \&\approx \boxed{950}\end{align*}\)

Therefore, the projected number of new cases for 2008 is 950.

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Answer:

Very straightforward! Although we don't know actual dollar amounts, we only need fractions. Multiply the 3/4 of her allowance by the 5/6 of spending that was gummy bears:

3 * 5                         Cancel the 3 and 6, dividing each by 3:

4    6

1 * 5                         Nothing else cancels, so just multiply sideways as usual, and you get:

4    2

5

8

Upvote

•

1

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Add comment

Step-by-step explanation:

Very straightforward! Although we don't know actual dollar amounts, we only need fractions. Multiply the 3/4 of her allowance by the 5/6 of spending that was gummy bears:

3 * 5                         Cancel the 3 and 6, dividing each by 3:

4    6

1 * 5                         Nothing else cancels, so just multiply sideways as usual, and you get:

4    2

5

8

Upvote

•

1

Downvote

Add comment

Answer: spent on gummy bears = 3/4 * 5/6 = 15/24 =5/8 of weekly allowance

Answer:

39.   An adult male Western Banded Gecko is 5 1/2 (or 5.5) inches long.

41.    13,000 feet long, because 1 4/9 of 9,000 is 13,000.

43.  to answer the question we need to know if 35 out of 50 states is equal or greater than 3/4 if that is the case, the Constitution will be ammended, and that is represented like this:

35/50 >= 3/4

that inequality is saying that 35 states out of 50 is equal or greater than 3/4, lets simplify and modify the fractions to compare easily:

35/50 >= 3/4

7/10 >= 3/4

now we need to find the least common multiplier of 10 and 4 to take the fractions to a common denominator and compare easy. Lets multiply numerator and denominator for a correct number to get the fractions to denominator common 20, the lcm:

7/10 >= 3/4

(2/2)(7/10) >= (5/5)(3/4)

2*7/2*10 >= 5*3/5*4

14/20 >= 15/20

we can see that the inequality does not hold, so,

35/50 >= 3/4

does not hold either, therefore the Constitution cannot be ammended

40.  10 students play chess and sudoku,

30*2/5 is 12, out of 12; the number of students that play chess,5/6 play sudoku.

So..12*5/6 is 10 and that is the number of students that play both sudoku and chess.

42. Four fifths of 7/8 will be less than 7/8 (because you've multiplied by a number less than 1).

Similarly, 7/8 of 4/5 will be less than 4/5.

This means that the product will be less than each of the original factors.  

answer: no

44.  The answer is 7/12 because 3/4 - 1/6= 7/12

3/4 converts to 9/12 and 1/6 converts to 2/12. The domanaters stay the same, but 9-2=7. that is how you get 7/12

The objective of keyword bidding is to d. get the best ranking for the lowest cost.

Keyword bidding is a practice used in online advertising, specifically in pay-per-click (PPC) campaigns, where advertisers bid on specific keywords to display their ads in search engine results. The objective of keyword bidding is to achieve the best possible ranking for their ads while keeping the cost as low as possible.

Option (a), obtaining the most profitable domain name, is not related to keyword bidding. Domain names refer to the website address or URL and are not directly associated with keyword bidding.

Option (b), limiting the amount of money the firm spends on search marketing, is partially correct but not the primary objective. While controlling costs is important, the main goal of keyword bidding is to optimize the ranking and visibility of ads.

Option (c), always being ranked first, is not feasible for every advertiser. Search engine rankings are determined by various factors, including bid amount, quality score, and relevance. It is not guaranteed that an advertiser will always secure the top position.

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Answer:

  $808.76

Step-by-step explanation:

You want the simple interest earned on $1975 at the rate of 9.1% per year for 4.5 years.

The amount of simple interest is given by the formula ...

  I = Prt

where principal P is invested at rate r for t years.

Using the given values, the amount of interest earned is ...

  I = $1975·0.091·4.5 = 808.7625 ≈ $808.76

The amount of simple interest is $808.76.

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The y-intercept represents the initial temperature of the liquid before cooling  and the slope represent the changes in temperature for every m minutes.

y = 100 - 5m

where

y = temperature in degree Celsius

m = cooling for number of minutes

Using the slope intercept equation,

where

m = slope

b = y-intercept

Therefore,

y - intercept = 100

slope(m) = 5

Therefore, the y-intercept represents the initial temperature of the liquid before cooling  and the slope represent the changes in temperature for every m minutes.

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Answer:

360 feet.

Step-by-step explanation:

Let x = length, then the width is 4x/9 feet.

So we have the equation:

x * 4x/9 = 57600

4x^2 / 9 = 57600

4x^2 = 57600 * 9

x^2 = 57600 * 9 / 4

x = √57600 * 3 / 2

x = 240* 3/2

x = 360 feet.

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.

The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.

In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:

Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}

Favorable outcomes (multiples of 3): {3, 6}

The total number of possible outcomes is 6, and the number of favorable outcomes is 2.

The theoretical probability of spinning a multiple of 3 can be calculated as:

P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(multiple of 3) = 2 / 6

Simplifying the fraction, we get:

P(multiple of 3) = 1 / 3

Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.

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Answer:

The speed of sound is 2.23 times of the speed of race car

Step-by-step explanation:

Given that,

The speed of a race car = \(3.4\times 10^2\ mi/h\)

The speed of sound = \(7.6\times 10^2\ mi/h\)

Dividing the speed of sound to the speed of a race car. So,\(\dfrac{\text{speed of sound}}{\text{speed of race car}}=\dfrac{7.6\times 10^2}{3.4\times 10^2}\\\\\dfrac{\text{speed of sound}}{\text{speed of race car}}=2.23\)

So, the speed of sound is 2.23 times of the speed of race car.

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

9514 1404 393

Answer:

  $1320

Step-by-step explanation:

The amount of commission is the product of the commission rate on sales and the amount of sales:

  Job A commission = 0.12 × $11,000 = $1320

_____

It may help you to realize that the percent symbol (%) is fully equivalent to /100. That is 12% = 12/100 = 0.12.

Answer: The amount of carbon-14 remaining after a certain amount of time can be modeled by the exponential decay function:

N(t) = N0 * e^(-kt)

where N0 is the initial amount of carbon-14, k is the decay constant, and t is the time elapsed since the death of the organism.

We know that the half-life of carbon-14 is 5730 years. This means that the amount of carbon-14 remaining after one half-life is:

N(5730) = 0.5N0

Solving for the decay constant k, we get:

0.5N0 = N0 * e^(-k * 5730)

0.5 = e^(-k * 5730)

ln(0.5) = -k * 5730

k = ln(2) / 5730

Now, we can use the fact that the skeleton has 20% of its original carbon-14 remaining to solve for the time since death. Let T be the time elapsed since death. Then, we have:

N(T) = 0.2N0 = N0 * e^(-k * T)

Solving for T, we get:

T = -ln(0.2) / k

Plugging in the value of k, we get:

T = -ln(0.2) / (ln(2) / 5730) ≈ 17089 years

Therefore, the human died approximately 17089 years ago.

Step-by-step explanation:

Answer:

So the equation and solution will be:

Total time taken = 3 × number of shirts + 19.87 min (setup time)

                            = 3 × 143 + 19.87

                           \(=429+19.87\)

                             \(=448.87\)

Step-by-step explanation:

From the question statement, it is clear that

we have to determine how long does it take to screen-print a batch of 143 shirts.

so the equation and solution will be:

Total time taken = 3 × number of shirts + 19.87 min (setup time)

                           = 3 × 143 + 19.87

                           \(=429+19.87\)

                             \(=448.87\)  min

Answer:

C

Step-by-step explanation:

It goes down from right to left so the slope will be negative, and the y-intercept (or where the line touches the y axis) is 2, so the only one that works is C.

a) The 90% confidence interval for the population mean is approximately 34.52 to 37.48.

b) The 95% confidence interval for the population mean is approximately 34.23 to 37.77.

c) The 99% confidence interval for the population mean is approximately 33.68 to 38.32.

a. 90% confidence interval:

A 90% confidence interval means that if we were to repeat this sampling procedure multiple times, approximately 90% of the intervals calculated would contain the true population mean. The standard error (SE) represents the standard deviation of the sample mean and is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n).

Plugging in the values:

Confidence interval = 36 ± (1.645 * (7 / √60))

Confidence interval ≈ 36 ± (1.645 * 0.903)

Confidence interval ≈ 36 ± 1.487

Confidence interval ≈ 34.52 to 37.48

b. 95% confidence interval:

Similarly, to calculate a 95% confidence interval, we use a different critical value. For a 95% confidence level, the critical value is approximately 1.96. Applying the formula:

Confidence interval = 36 ± (1.96 * (7 / √60))

Confidence interval ≈ 36 ± (1.96 * 0.903)

Confidence interval ≈ 36 ± 1.771

Confidence interval ≈ 34.23 to 37.77

c. 99% confidence interval:

To calculate a 99% confidence interval, we use a higher critical value. For a 99% confidence level, the critical value is approximately 2.576. Applying the formula:

Confidence interval = 36 ± (2.576 * (7 / √60))

Confidence interval ≈ 36 ± (2.576 * 0.903)

Confidence interval ≈ 36 ± 2.326

Confidence interval ≈ 33.68 to 38.32

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The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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Answer:

the 4th and 6th one

Step-by-step explanation:

A function is when there are x- and y-values but each x value has only 1      y-value

Simple: If the x-value is repeated its not a function

Answer:

Step-by-step explanation:

1,2,3

To convert the system into an augmented matrix, we can represent the given equations as follows:

1   -5   4   |  22

2   -12  4   |  8

To reduce the system to echelon form, we'll perform row operations to eliminate the coefficients below the main diagonal:

R2 = R2 - 2R1

1   -5   4   |  22

0   -2   -4  |  -36

Next, we'll divide R2 by -2 to obtain a leading coefficient of 1:

R2 = R2 / -2

1   -5   4   |  22

0   1    2   |  18

Now, we'll eliminate the coefficient below the leading coefficient in R1:

R1 = R1 + 5R2

1   0    14  |  112

0   1    2   |  18

The system is now in echelon form. To determine if it is consistent, we look for any rows of the form [0 0 ... 0 | b] where b is nonzero. In this case, all coefficients in the last row are nonzero. Therefore, the system is consistent.

To find the solution, we can express x1 and x2 in terms of the free variable s1:

x1 = 112 - 14s1

x2 = 18 - 2s1

x3 is independent of the free variable and remains unchanged.

Therefore, the solution is (x1, x2, x3) = (112 - 14s1, 18 - 2s1, s1), where s1 is any real number.

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The correct graph of amounts of water plot the measurements on a line plot is shown in image.

We have to given that;

The amounts of water plot the measurements on a line plot are,

1/8 oz, 1/8 oz, 1/4 oz, 1./4 oz, 1/4 oz, 1/2 oz, 1/2 oz , 1/2 oz, 3/4 oz, 1 oz

Now, We have;

1/8 oz is repeats two times.

1/4 oz is repeats three times.

1/2 oz is repeats two times.

3/4 oz is only one times

And, 1 oz is repeats one time.

Thus, The correct graph of amounts of water plot the measurements on a line plot is shown in image.

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Answer:

125 km per hour

Step-by-step explanation:

divide 500 by 4 to find the averge

Answer:

\( \sf \: 125km/hr\)

Step-by-step explanation:

Average speed = \( \sf \: \frac{distance \: travelled}{time \: taken} \)

Ave. speed = \( \sf \frac{500km}{4hr} = 125kmhr {}^{ - 1} \)

Hence, the average spred is 125km/h respectively.

The working of T critical value calculator is explained

What is t test?

t test is the test used  if the sample standard deviation is known and population standard deviation is unknown.

t test is used if the sample standard deviation is known and population standard deviation is unknown.

Here, t value is calculated by the formula

\(t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(\bar{x}\) = mean of the sample

\(\mu\) = mean of the population

s = standard deviation of sample

n = Number of samples

Now, with the help of degree of freedom (n - 1) and the level of significance, the critical value of t is to be noted from the t table. Let it be \(t_{critical}\)

if the value of t lies between \(-t_{critical}\) and \(+t_{critical}\) then the null hypothesis is accepted, otherwise the null hypothesis is rejected.

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Given, the function is f(x,y,z)=5+yxz+g(x,z)Here, we need to find the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) . The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

Using the formula of the directional derivative, the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is given by

(f(x,y,z)) = grad(f(x,y,z)).v

where grad(f(x,y,z)) is the gradient of the function f(x,y,z) and v is the direction vector.

∴ grad(f(x,y,z)) = (fx, fy, fz)

                       = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Hence, fx = ∂f/∂x = 0 + yzg′(x,z)fy

                = ∂f/∂y

                = xz and

fz = ∂f/∂z = yx + g′(x,z)

We need to evaluate the gradient at the point (3,0,3), then

we have:fx(3,0,3) = yzg′(3,3)fy(3,0,3)

                             = 3(0) = 0fz(3,0,3)

                             = 0 + g′(3,3)

                             = g′(3,3)

Therefore, grad(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))Dv(f(x,y,z))(3,0,3)

                                                 = grad(f(x,y,z))(3,0,3)⋅v

where, v = (0,4,0)Thus, Dv(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))⋅(0,4,0)   = 0

The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

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ANSWER

[5, ∞)

EXPLANATION

First we have to solve each inequality separately:

And the other inequality

Graphing this solution set:

Solution x ≥ 5 includes solution x ≥ 1, so the solution is [5, ∞)