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Answer: The two numbers are $x = 5$ and $y = 7.5$.

Step-by-step explanation:

Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:

$$2y = 3x + 15$$

$$\frac{1}{5}x + \frac{1}{9}y = 10$$

We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get

$$10y = 15x + 75$$

$$9x + y = 90$$

Subtracting these equations, we get

$$8y - 9x = 15$$

Multiplying this equation by 8, we get

$$64y - 72x = 120$$

Adding this equation to 5 times the first equation, we get

$$69y - 72x = 120 + 75$$

$$69y - 72x = 195$$

Dividing both sides by 3, we get

$$23y - 24x = 65$$

Subtracting this equation from 4 times the second equation, we get

$$96y - 36x = 360 - 260$$

$$96y - 36x = 100$$

Dividing both sides by 60, we get

$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$

Substituting the expression for $y$ from the first equation, we get

$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$

This simplifies to

$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$

Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.

Answer:

y = 10

Step-by-step explanation:

given DEFG = SPQR

QR = FG

=> 2x - 4 = 12

=> 2x = 16

=> x = 8

angle PQR = EFG

=> 6y + x = 68

=> 6y + 8 = 68

=> 6y = 60

=> y = 10

This is a simple cross multiplication problem! Any time you're given a ratio and then the actual quantity of something, you can use cross multiplication to figure out the quantity of the other thing!

We know that the ratio of toads to frogmen is 7 : 2. We also know there were 98 actual toads. Therefore we can set up our equations!

[tex]ratio_{toads}=ratio_{frogmen}\\actual_{toads}=actual_{frogmen}\\\\7=2\\98 = x\\\\7x=196\\x=28[/tex]

The first two equations above everything is how you would have everything set up! The second equations under them are the numbers plugged in, and the rest is just simplification.

So, your final answer should be 28 frogmen!

The given statement can be written as expression given by -

y = 3 ÷ (4 - x)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the statement as -

"3 is divided by the difference of 4 and a number"

Assume the number to be {x}. Then, we can write the expression as -

3 ÷ (4 - x)

Let this expression is equivalent to {y}. We can write -

y = 3 ÷ (4 - x)

Therefore, the given statement can be written as expression given by -

y = 3 ÷ (4 - x)

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Step-by-step explanation:

please refer to the 3 pages of sketch for details

The total length of the two boards put together is 5ft 11in.

Length is a measure of distance. It is typically measured in units such as inches, feet, yards, miles, millimeters, centimeters, and meters. Length can also be measured in other units, such as the amount of time it takes to travel a certain distance. Length is an important concept in mathematics and is used in many different topics and applications.

To simplify this answer in feet, we can convert the 10 inches and 9 inches to feet, giving us a total of 5 feet. Therefore, the total length of the two boards put together is 5ft.

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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.

Given expression,

= 4 1/3 / (-5/6 )

= (13/3 )/ (-5/6)

= 13*6 / -15

= -26/5

By evaluating the other expressions to find its equivalent,

(13 / 3) / (-5/6)

= 13 * 6 / -15

= -26/5

Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .

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On solving the provided question, we can say that we can assume that it is a rectangular backyard. Since no dimensions are provided therefore, neither volume nor area can be calculated.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

we can assume that it is a rectangular backyard.

since no dimensions are provided therefore, neither volume nor area can be calculated.

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Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).

The mathematical field of trigonometry investigates relationships between triangle sides and angles. Because every straight-sided form may be reduced to a collection of triangles, trigonometry is a fundamental concept in all of geometry. The relationships between trigonometry and other branches of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly intricate.

Here,

[tex]e^{x}[/tex] is a function that increases across all of space  (d[[tex]e^{x}[/tex] ]/dx = [tex]e^{x}[/tex]  which is never negative), it must be that so it must be that [tex]e^{u}[/tex] crosses y=1 just once, or at u = 0. To demonstrate this:

In[tex]e^{sinx}[/tex]= In 1

sin x = 0

And when x = "0, 0", "2", we would have that sin x = 0 in [0, 2"]. In general, we would then have that x = n, where n Z, because of the periodicity of sin (where n is an integer).

Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).

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Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.

Here,

are the definitions of each equation:

1. x^2 + y^2 - 4x + 6y - 5 = 0

 The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.

2. x^2 - 6y = 0

 The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.

3. 4x^2 + 9y^2 = 1

This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.

4. 7x^2 - 9y^2 = 343

 A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.

Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

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The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Advantages include:

Disadvantages:

Additional expenses include

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Answer:

See below

Step-by-step explanation:

Absolute value is the positive distance from 0, so |-7| = 7 because -7 is 7 from 0, whereas 6 is 6 away from 0. Because 7>6, then -7 has a greater absolute value than 6

If you list the number of tickets sold over time, the kind of sequence which you would see include the following: B. geometric.

In Mathematics, a geometric sequence can be defined as a series of real and natural numbers that are calculated by multiplying the next number by the same number (common or constant ratio) each time.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Assuming the variable x represents the number of ticket sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression which models this situation is given by geometric sequence:

x, 7x, 49x, 343x, .....

Check:

7/1 = 49/7 = 343/49 = 7 (proof).

Therefore, this is a geometric sequence.

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Complete Question:

A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?​

arithmetic

geometric

both

neither

Answer:

The answer is zero

Step-by-step explanation:

Hope it helps

Answer:

Yes

Step-by-step explanation:

A $79 unit plus HST will be 89.27

[tex]\dfrac{s}{4} +5=13[/tex]

Simplify:

[tex]\dfrac{1}{4} s+5=13[/tex]

Subtract 5 from both sides:

[tex]\dfrac{1}{4} s+5-5=13-5[/tex]

[tex]\dfrac{1}{4} s=8[/tex]

Multiply both sides by 4:

[tex]4\times(\dfrac{1}{4} s)=4\times(8)[/tex]

[tex]\fbox{s = 32}[/tex]

s = 32.

[tex]\frac{s}{4} +5=13[/tex]

[tex]\frac{s}{4} +5-5=13-5\\ \\\frac{s}{4} =8[/tex]

[tex]\frac{s}{4}*4 =8*4\\ \\s=32[/tex]

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "s" by it's calculated value, 32.

[tex]\frac{(32)}{4} +5=13\\ \\8+5=13\\ \\13=13[/tex]

As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!

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A) The ratios for 2021 are as follows:

Rate of return on total asset = (Profit for the year / Total assets) * 100 = (12,605 / 29,935) * 100 = 42%

Profit margin ratio = (Profit for the year / Revenue) * 100 = (12,605 / 55,000) * 100 = 22.9%

Current ratio = (Current assets / Current liabilities) = (17,190 / 7,700) = 2.23:1

Inventory turnover ratio = (Cost of sales / Inventory) = (35,100 / 3,675) = 9.58

Accounts receivable turnover ratio = (Revenue / Receivables) = (55,000 / 4,905) = 11.22

Debt ratio = (Total liabilities / Total assets) = (15,720 / 29,935) = 52.6%

Times interest earned = (EBIT / Interest) = (12,715 / 1,560) = 8.14

B) Based on the above industry averages:

profitability: the company's profit margin ratio of 22.9% is lower than the industry average of 40%, which suggests that the company's profitability is lower than the industry average.

liquidity: the company's current ratio of 2.23:1 is lower than the industry average of 2.5:1, which suggests that the company's liquidity is lower than the industry average.

use of financial gearing: the company's debt ratio of 52.6% is higher than the industry average of 6%, which suggests that the company is more heavily leveraged than the industry average.

In summary, the company profitability is lower than the industry average, liquidity is lower than the industry average, and the company is more heavily leveraged than the industry average.

A company's profitability refers to its ability to generate a profit and return on investment. It is a measure of how well a company is able to generate revenue, control costs, and manage its assets and liabilities. Profitability ratios are used to evaluate a company's financial performance and to compare it to other companies in the same industry. Some of the most common profitability ratios include:

Gross profit margin: measures the percentage of revenue that remains after accounting for the cost of goods sold. It's calculated by dividing gross profit by revenue.

Operating profit margin: measures the percentage of revenue that remains after accounting for all operating expenses. It's calculated by dividing operating profit by revenue.

Net profit margin: measures the percentage of revenue that remains after accounting for all expenses, including taxes and interest. It's calculated by dividing net profit by revenue.

Return on assets (ROA): measures how efficiently a company is using its assets to generate a profit. It's calculated by dividing net income by total assets.

Return on equity (ROE): measures how efficiently a company is using shareholder's equity to generate a profit. It's calculated by dividing net income by shareholder's equity.

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Simplifying the expression, the answer would be -7x+1

Solution

3 (x+2) - 5 (2x+1)

3x + 6 - 10x -5

COLLECT LIKE TERMS

3x - 10x + 6 - 5

= -7x+1

Answer:

Step-by-step explanation:

-140

The answer to |-14| is 14

Answer:

Y less than

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.124

The probability that they include at least five persons having blood of type O is given as follows:

0.1075 = 10.75%.

The number of donors needed so that the probability of including at least one student donor of type O shall be 0.9 or more is of 184 donors.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

n = 200, p = 1/80 = 0.0125.

The probability of less than five is given as follows:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Using a binomial distribution calculator, these probabilities are given as follows:

Hence the probability of less than five successes is given as follows:

P(X < 5) = 0.0808 + 0.2046 + 0.2576 + 0.2153 + 0.1342 = 0.8925.

Hence the probability of at least five is given as follows:

P(X >= 5) = 1 - P(X < 5) = 1 - 0.8925 = 0.1075.

The probability of at least one is given as follows:

P(X >= 1) = 1 - P(X = 0)

P(X >= 1) = 1 - (1 - 0.0125)^n.

This probability is of 0.9 when:

1 - (1 - 0.0125)^n = 0.9

(0.9875)^n = 0.1

log((0.9875)^n) = log(0.1)

nlog(0.9875) = log(0.1)

n = log(0.1)/log(0.9875)

n = 183.1.

Rounding up, at least 184 donors must be surveyed.

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Answer:

Step-by-step explanation:

If Colton makes a guaranteed salary of $500 per week, and he is paid a commission of 10% on top of that for a total of $1075 in sales, he would make an additional $107.50 in commission (1075 x .1 = 107.5). In total, Colton would make 500 + 107.5 = $607.50 in a week where he made $1075 in sales.

Answer:

800 hrs = 33.3 days

Step-by-step explanation:

1 day = 24 hours

800 hours = 800/24 = 33.33

Round to the nearest tenth:

33.3 days

Answer: $1794.28

Step-by-step explanation:

280*5.95= 1666

0.077*1666= 128.282

1666+128.282= 1794.282

We round cause its money

Answer: A. Quadrilateral

Step-by-step explanation:

The name for a polygon with 4 sides is a quadrilateral. Quadrilateral is a two-dimensional shape with four straight sides and four angles. The most common type of quadrilateral is the rectangle, which has four right angles. Other types of quadrilaterals include squares, parallelograms, trapezoids, and rhombuses.

Answer:

quadrilateral!!

Step-by-step explanation:

look at the beginning of the word, quad. Quad means 4 and is referring to a 4 sided figure.

a) The process to find the limit is given as follows:

b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

Hence:

For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.

Applying the subtraction of perfect squares, we have that:

x² - 1 = (x - 1)(x + 1).

Then:

g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.

Meaning that the limit is then calculated as follows:

lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.

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The length of the side CD is 5.195 cm and the Area of ΔABC is 31.17 cm²

The basic trigonometric functions are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the given triangle ABC, we can see that it is a right angle triangle where ∠ACD = 60°, and as such, ∠CAD = 30°.

Thus;

BC/AC = tan 30°

6/AC = 0.5774

AC = 10.39cm

Thus;

CD/AC = cos 60

CD = 10.39 * 0.5

CD = 5.195 cm

Formula for area of a triangle is;

Area = ¹/₂ * base * height

Area = ¹/₂ * 6 * 10.39

Area = 31.17 cm²

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Answer: 10,000

Step-by-step explanation: here's how I got my answer:

Since we are finding the decrease from 2005-2015, we need to multiply 1/20 by 10, since the timespan is 10 years worth of decreasing.

So, 1/2 * 10 =1/2

So, since we have 1/2 as the overall decrease in the population within the 10 years, we divide 20,000 by 1/2 or 20,000 by 2, and we get 10,000. I hope this helps.

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square  or 49π meter square option 1 is correct.

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

Given :

Diameter of circle : 14

Radius =14/2 =  7 meters

and

Using formula

Area= πr²

=> Area = π7²

=>Area = 22/7 * 7²

=> Area = 22*7

=> Area = 154 meter square or 49π meter square

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square  or 49π meter square option 1 is correct.

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Answer: A the first one 49π square meters