10x + 7y = -3
5x - y = 3

Answer:

432 aquariums

Step-by-step explanation:

To determine the number of aquariums the factory made, find the volume of 1 aquarium, then divide the total volume of water required.

Solution:

Volume of triangular prism aquarium = triangular base area × length of triangular prism

Volume = ½*b*h*l

Where,

b = 8 ft

h = 4 ft

l = 3 ft

Volume = ½*8*4*3 = 4*4*3

Volume = 48 ft³

Number of aquarium made = Volume of water required ÷ volume of 1 aquarium

= 20,736 ÷ 48 = 432 aquariums

Answer:

your range is -9 to positive 5

Step-by-step explanation:

range is how many numbers are in a squence for example i have 1 2 3 so my range is 1-3

Answer:

Step-by-step explanation:

6

Answer:

they did not meet their goal

Step-by-step explanation:

The given expression (-3. 8)+0+y would yield the following values, if evaluated for the mentioned values of y. If y = -3.3, the value is -7.1, If y = -7.1, the value is -10.9 , If y = -2.6, the value is -6.4 , If y = 1, the value is -2.8. and If y = 4.2, then the value is 0.4.

To evaluate the funtion (-3.8) + 0 + y for the given values of y, we substitute the values of y one by one and simplify:

In order to calculate  y = -3.3, putting the values of y in the given expression,

= (-3.8) + 0 + (-3.3) = -7.1

Now for y = -7.1, the expression can be evaluated as

=(-3.8) + 0 + (-7.1) = -10.9

For the calculation of y = -2.6,

=(-3.8) + 0 + (-2.6) = -6.4

Calculating y = 1, we will get,

=(-3.8) + 0 + 1 = -2.8

And finally for y = 4.2

= (-3.8) + 0 + 4.2 = 0.4

Therefore, the resultant values of the expression (-3.8) + 0 + y for the given values of y are:

For y = -3.3, the value is -7.1.

For y = -7.1, the value is -10.9.

For y = -2.6, the value is -6.4.

For y = 1, the value is -2.8.

For y = 4.2, the value is 0.4.

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Answer:

D

Step-by-step explanation:

The slope is 2 and the y-intercept is -3

The slope of the equation and y- intercept​ is 320 and 1500 respectively.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Given that the total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking.

To find the slope and y- intercept​.

y=320x+1500

Therefore, the slope of the line is;

m =320

Then the y- intercept is 1500

Hence, The slope of the equation and y- intercept​ is 320 and 1500 respectively.

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Answer:

What does 134 x-7 equal?

134 x -7

Step-by-step explanation:

You're welcome.

Answer:

8

Step-by-step explanation:

Step 1: Write polynomial

4x⁵ - 16x² + 13x⁸

Step 2: Rearrange

13x⁸ + 4x⁵ - 16x²

The degree of a polynomial is the highest power. In this case, our degree would be 8 because of the x⁸ term being the largest exponent.

Answer:

4x-3=x+2

4x-x=3+2

3x=5

x=5/3

Using the formula for gravitational force on Mars, determine the weight of the astronaut on the surface of Mars, which is approximately 358.6 N.

To calculate the weight of the astronaut on the surface of Mars, we can use the formula for gravitational force:

\(F = (G * m_1 * m_2) / r^2\)

Where:

F is the gravitational force,

G is the gravitational constant (approximately \(6.67430 * 10^{-11} N m^2/kg^2\)),

\(m_1\) is the mass of the astronaut,

\(m_2\) is the mass of Mars,

and r is the radius of Mars.

Mass of Mars (\(m_2\)) = \(6.39 * 10^{23} kg\)

Radius of Mars (r) = 3376.2 km = 3,376,200 meters

Weight on Earth = 950 N

950 N = (G * mass of the astronaut * mass of Earth) / radius of Earth^2

mass of the astronaut = (950 N * radius of Mars^2 * mass of Mars) / (radius of Earth^2 * mass of Earth)

\(F = (G * m_1 * m_2) / r^2\)

First, let's convert the radius of Mars from kilometers to meters:

r = 3,376,200 meters

Next, we can rearrange the formula to solve for m1:

\(m_1 = (F * r^2) / (G * m_{2})\)

\(m_1 = (950 N * (3,376,200 m)^2) / ((6.67430 * 10^{-11} N m^2/kg^2) * (6.39 * 10^{23 }kg))\\m_1 = 78.656 kg\)

Weight on Mars =\((G * m_1 * m_2) / r^2\)

Weight on Mars = \((6.67430 * 10^{-11}N m^2/kg^2) * 78.656 kg * \frac{ (6.39 * 10^{23} kg)}{(3,376,200 m)^2}\)

Weight on Mars ≈ 358.6 N

Therefore, the weight of the astronaut on the surface of Mars would be approximately 358.6 N.

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The two integers are 11 and 17. 11 is the smaller integer and 17 is the larger integer. The reciprocal of 11 is 1/11 and the reciprocal of 17 is 1/17. 10 times the reciprocal of 17 is 10/17, and subtracting the reciprocal of 11 (1/11) from 10/17 results in 37.

1. The problem states that the smaller integer is 6 less than the larger integer, meaning that 17 is 6 more than 11.

2. The reciprocal of 11 is 1/11 and the reciprocal of 17 is 1/17.

3. 10 times the reciprocal of 17 is 10/17, and subtracting the reciprocal of 11 (1/11) from 10/17 results in 37.

4. We can set up two equations: 1/11 + 10/17 = 37 and 11 + 17 = x.

5. We can solve for x by multiplying both sides of the second equation by 17, giving us 187 = x.

6. We can now substitute this result into the first equation, giving us 1/11 + 10/17 = 187.

7. We can then solve for 11, giving us 11 = 176/17.

8. We can then solve for 17, giving us 17 = 11.

9. We can now see that 11 and 17 are the two integers that satisfy the problem.

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The general solution of an associated homogeneous differential equation is yh(x) = c1e^(-2x)cosx + c2e^(-2x)sinx and general solution to the original non-homogeneous differential equation is y(x) = c1e^(-2x)cosx + c2e^(-2x)sinx + (3/2) e^-x.

Given the differential equation:

y''+4y'+5y=-15x+3e^-x.

a) We have the characteristic equation as:

r^2 + 4r + 5 = 0

The roots of the above quadratic equation are:

r = -2 + i and r = -2 - i

Therefore, the solution to the associated homogeneous differential equation:

yh(x) = c1e^(-2x)cosx + c2e^(-2x)sinx (where c1 and c2 are arbitrary constants)

Finding particular solution to the non-homogeneous differential equation:For non-homogeneous differential equation:

y''+4y'+5y=-15x+3e^-x

Let’s find the solution yp(x) using the method of undetermined coefficients. We have:

yp(x) = [(-15x + 3)/ A^2 + 4A + 5] x + (B/A^2 + 4A + 5) e^-x, where A and B are unknown constants, we have to find.

According to the undetermined coefficients method, as we have a term in the non-homogeneous differential equation of the form e^-x, thus we will consider the trial solution for yp(x) in the form:

yp(x) = C1 e^-x

Differentiating yp(x) to x, we get:

yp'(x) = -C1 e^-x

Differentiatingyp(x) again) with respect to x, we get:

yp''(x) = C1 e^-x,

Putting these values in the non-homogeneous differential equation, we get:

C1 e^-x + 4(-C1 e^-x) + 5(C1 e^-x) = 3e^-x-15x

Comparing the coefficients of both sides, we have:

C1 [1 + (-4) + 5] = 0

∴ C1 = 3/2

Therefore, the solution is: yp(x) = (3/2) e^-x. Now, adding the particular solution and general solution of the associated homogeneous equation, we get the general solution of the non-homogeneous differential equation:

y(x) = c1e^(-2x)cosx + c2e^(-2x)sinx + (3/2) e^-x

Thus, we have found that the particular solution to the nonhomogeneous differential equation is yp(x) = (3/2) e^-x, the general solution of associated homogeneous differential equation is yh(x) = c1e^(-2x)cosx + c2e^(-2x)sinx and the general solution to the original nonhomogeneous differential equation is y(x) = c1e^(-2x)cosx + c2e^(-2x)sinx + (3/2) e^-x.

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3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

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Step-by-step explanation:

Principal = 250,000

Rate = 4%

Simple interest = 850,000

Time = ?

\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)

you cannot divide by 0

so solve

y(z+5)=0

y=0 and z+5=0

y=0 and z=-5

excluded values are y=0 and z=-5

Have a great day

Answer:

Step-by-step explanation:

Let a, b, c represent the amounts received by the first, second, and third person, respectively.

  2a-1 = b

  c = b+11

  a + b + c = 224

Substituting for c, we have ...

  a + b + b+11 = 224

  a +2b = 213

Substituting for b, we have ...

  a +2(2a -1) = 213

  a +4a -2 = 213 . . . . . eliminate parentheses

  5a = 215 . . . . . . . . . . add 2

  a = 43 . . . . . . . . . . . . .divide by 5

  b = 2a -1 = 2(43) -1 = 85

  c = b +11 = 85 +11 = 96

The amounts received were ...

The new limits of integration c and d, in that order, are: 0 and 5.

The functions g(y) and h(y), in that order, are: 0 and 5y/2.

To reverse the order of integration for the iterated integral ∫₀²₅​∫₀^(2x/5)​​f(x,y)dydx, we need to determine the new limits of integration and the functions g(y) and h(y) that define the interval of y integration.

(a) The new limits of integration c and d can be found by considering the original limits of integration for x and y. In this case:

- For x: x ranges from 0 to 5.

- For y: y ranges from 0 to 2x/5.

Thus, new limits of integration c and d, in that order, are: 0 and 5.

(b) To determine the functions g(y) and h(y), we need to express the new limits of integration for y in terms of y alone. Since the original limits are dependent on x, we can use the relationship between x and y to express them solely in terms of y.

From the original limits of integration for y, we have:

0 ≤ y ≤ 2x/5.

Solving this inequality for x, we get:

0 ≤ x ≤ 5y/2.

Therefore, the functions g(y) and h(y), in that order, are: 0 and 5y/2.

The reversed iterated integral is:

∫₀⁵​∫₀^(5y/2)​​f(x,y)dxdy.

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To determine whether the series ∑(n=1 to infinity) 7n/n is convergent or divergent, we can apply the ratio test. The ratio test helps us determine the convergence or divergence of a series by examining the limit of the ratio of consecutive terms.

In this case, let's calculate the ratio of consecutive terms using the formula for the ratio test:

lim(n→∞) |(7(n+1)/(n+1))/((7n/n)|

Simplifying the expression, we get:

lim(n→∞) |7(n+1)/n|

As n approaches infinity, the limit evaluates to:

lim(n→∞) |7(n+1)/n| = 7

Since the limit is a finite positive value (7), which is less than 1, the ratio test tells us that the series is convergent.

However, you mentioned identifying an (term) in the series, and it seems there may be an incomplete part of the question. Please provide additional information or clarification about identifying an term in the series so that I can provide a more specific answer.

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The 90% confidence interval for the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is: resulting in a confidence interval of (4.337, 6.263) pounds.

To construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not, we can use a two-sample t-test with unequal variances.

The null hypothesis is that the true difference between the mean amounts of weight lost by the two groups is zero, and the alternative hypothesis is that the true difference is not zero.

We can use the following formula to calculate the confidence interval:

CI = (x_1 - x_2) ± tα/2 * √((s_1)²/n_1 + (s_2)²/n_2)

where

x_1 = 15.6 (mean amount of weight lost by group a)

x_2 = 10.3 (mean amount of weight lost by group b)

s_1 = 1.2 (standard deviation of group a)

s_2 = 1.9 (standard deviation of group b)

n_1 = n_2 = 26 (sample size of both groups)

tα/2 = t0.05/2,24 = 1.711 (degrees of freedom = n_1 + n_2 - 2 = 50)

Plugging in the values, we get:

CI = (15.6 - 10.3) ± 1.711 * √(1.2²/26 + 1.9²/26)

CI = 5.3 ± 0.963

CI = (4.337, 6.263)

Therefore, with 90% confidence, we can estimate that the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is between 4.337 and 6.263 pounds.

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer: (-2i+ √5)(-21-√-5) simplifies to -19√5 + 42i - 5.

Step-by-step explanation:

To simplify the expression (-2i+ √5)(-21-√-5), we can first use the distributive property to expand the product:

(-2i)(-21) + (-2i)(-√-5) + (√5)(-21) + (√5)(-√-5)

Simplifying each term, we get:

42i + 2i√-5 - 21√5 - √25

Note that √-5 can be written as √(-1)√5 = i√5, using the fact that √-1 = i. Also, √25 = 5, so we can substitute these values to get:

42i + 2i√5 - 21√5 - 5

Combining like terms, we have:

(2i√5 - 21√5) + (42i - 5)

-19√5 + 42i - 5

Answer: $1200

Step-by-step explanation:

SO we know that their income is 5000 and 25% of it i for food.

so we will multiply 25% * 5000 =1250  so we know that  out of the 5000, $1250 - $50=$1200

This means that 1% of the was reduce.So now the food budget will be 24% out of the total budget.

Answer:

Step-by-step explanation:

The sale amount is:

The amount of commission:

Answer:

$ 56.50

Step-by-step explanation:

Sale amount = $ 950 = 500 + 450

Commission for $ 500 = 5% of 500 = 0.05 *500 = $25

Commission for sales over $ 500 = 7% of 450 = 0.07 * 450 = $ 31.50

Total commission =  25  + 31.50 = $56.50

1. Newmont Mining Corporation is a mining company, but the comparison company has not been specified. Therefore, I am unable to provide specific calculations or comparisons.

2. The three ratios that determine Return on Equity (ROE) can be used to compare and contrast the ROE values of the two companies once the comparison company is selected.

3. The top three risks identified by Newmont Mining Corporation can be found in their 10-K report.

1. Without knowing the specific comparison company within the same industry, I cannot perform calculations or provide a detailed comparison of ratios. Once the comparison company is specified, financial ratios such as liquidity ratios (current ratio, quick ratio), profitability ratios (gross profit margin, net profit margin), and leverage ratios (debt-to-equity ratio, interest coverage ratio) can be calculated for both companies to assess their relative strengths and weaknesses.

2. The three ratios that determine Return on Equity (ROE) are the net profit margin, asset turnover ratio, and financial leverage ratio. These ratios can be used to compare and contrast the ROE values of Newmont Mining Corporation and the selected comparison company. The net profit margin measures the company's profitability, the asset turnover ratio assesses its efficiency in generating sales from assets, and the financial leverage ratio evaluates the extent of debt used to finance assets.  

3. To identify the top three risks identified by Newmont Mining Corporation, one would need to review the company's 10-K report. The 10-K report is an annual filing required by the U.S. Securities and Exchange Commission (SEC) and provides detailed information about a company's operations, financial condition, and risks. Within the 10-K, the "Risk Factors" section typically outlines the significant risks faced by the company. By reviewing this section of Newmont Mining Corporation's 10-K report, the top three risks identified by the company can be identified, providing insights into the challenges and potential vulnerabilities the company faces in its industry.

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In a normal distribution, the median is approximately equal to its mean and mode. It means option (a) Approximately equal to is correct.

In a normal distribution, the mean, median, and mode are all measures of central tendency. The mean is the arithmetic average of the data, the median is the middle value when the data are arranged in order, and the mode is the most frequently occurring value. For a normal distribution, the mean, median, and mode are all located at the same point in the distribution, which is the peak or center of the bell-shaped curve.In fact, for a perfectly symmetrical normal distribution, the mean, median, and mode are exactly equal to each other. However, in practice, normal distributions may not be perfectly symmetrical, and there may be slight differences between the mean, median, and mode. Nevertheless, the differences are usually small, and the median is typically approximately equal to the mean and mode in a normal distribution.

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Answer:

Hoping someone else can answer with more confidence, but here's what I have:

on the left hand side:

upper is partial/penumbral lunar eclipse

lower is total solar eclipse

on the right hand side:

on the top: it's impossible for the moon to be behind the sun, so I'm not sure what they want there

middle is total solar eclipse

bottom is partial/penumbral lunar eclipse

Hope I helped at least a little

In grade 7, students will encounter mixed fraction addition, subtraction, multiplication, and division word problems.

When adding or subtracting mixed fractions, follow these steps:

Convert the mixed fractions into improper fractions.

Find a common denominator for the fractions involved.

Perform the addition or subtraction operation on the numerators, while keeping the common denominator.

Simplify the resulting fraction, if possible, by reducing it to its simplest form or converting it back to a mixed fraction.

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Answer:

i think its 8z-9 if im not wrong :)

Step-by-step explanation: