The graph below
Which equation matches the graph?

(I know that for sure! <3)

Assuming that the cost price in the question is 80K with a 65% profit percentage on cost price, the selling price of the shoe is 132K.

Given, Cost Price (CP) of the shoe = 80K or 80,000

           Profit % = 65%

From the formula, we know,

             Profit % = (Profit / Cost Price) * 100

Inserting given values in the formula, we get,

             ==>  65 = (Profit / 80,000) *100

                or, 65 = Profit / 800

Therefore, Profit = 65 * 800

                           = 52,000

In the case of Profit, Selling Price = Cost Price + Profit

Hence, the Selling Price of the shoe is = 80,000 + 52,000

                                                                 = 132,000 or 132K (Answer)

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Quadratic Expression: is an expression with the variable with the highest exponent being 2

General form: ax^2 + bx + c

Greatest common factor (GCF): the largest whole number that divides evenly into a set of numbers

When factoring out the GCF of this expression we must look at the "a" term and "c" term

[tex]8(x^2-3)[/tex] which is the expression factored.

Answer:20

Step-by-step explanation:

To estimate the number of buses Jamie needs, he can divide the total number of people going to the picnic by the number of people each bus can carry:

1,344 ÷ 56 ≈ 24 buses.

To check if using compatible numbers makes sense, Jamie can use 60 and 1,200, which are both multiples of 10 and closer to the actual numbers:

1,200 ÷ 60 = 20 buses.

Since 20 buses is less than the estimated 24 buses, Jamie will not have enough buses to transport all the people to the picnic. He may need to rent or borrow additional buses or find alternative transportation solutions.

It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.

How to solve the question?

Data collection is an essential aspect of research and analysis, as it involves gathering information from various sources to make informed decisions. Inaccurate data can lead to incorrect conclusions and flawed decision-making, which can have significant consequences. Therefore, it is crucial to determine the accuracy of the collected data.

Accuracy can be determined in several ways. One way is by how close repeated measurements of an attribute are to each other. This method is known as precision. If repeated measurements are consistent with one another, it indicates that the data is precise. However, precision does not necessarily imply accuracy, as the measured values could be consistently wrong.

Another way to determine accuracy is by how close repeated measurements are to the true value of the attribute being measured. This method is known as validity. Validity ensures that the collected data accurately reflects the attribute being measured. This method is often used in experiments to test the effectiveness of a treatment or intervention. The results of an experiment are valid if they accurately reflect the effects of the treatment or intervention being tested.

Accuracy can also be determined by how much deviation there is between the measured values and the true value. This method is known as error. An error is the difference between the measured value and the true value. The smaller the error, the more accurate the data.

In conclusion, accuracy in data collection is determined by how close the measured values are to the true value, how close repeated measurements are to each other, and how much deviation there is between the measured values and the true value. It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.

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Step-by-step explanation:

the arc lenght is usually described by the following formula:

[tex]l = \alpha \times r[/tex]

where l is the arc length, alpha the angle(in radians) and r is the radius.

so in this case, using this formula we get

[tex]l = 75 \times ( \frac{\pi}{180}) \times 5cm[/tex]

we are multiplying 75 x (pi/180) cuz, the angle has to be in radians. then

[tex]l = \frac{365}{180} \pi \: cm = 6.54 \: cm \: \: aprox[/tex]

more sensible than the last result, considering that the total length of the circle is

L=2(pi)r

in this case L= 31.4 cm aprox

Answer: (2, 3)

Step-by-step explanation:

The solution to a system of linear equations is where they intersect on a graph.

In this graph, the point of intersection is at (2, 3), so the answer is (2, 3).

Answer: To evaluate the line integral ∫CF⋅dr, we first need to parameterize the path C in terms of a single variable, say t. The parameterization of C is given by:

r(t) = (t^3, -3t^2, 2^t), 0 ≤ t ≤ 1

We can then write the differential of the path as:

dr = (3t^2, -6t, 2^t ln(2)) dt

Next, we evaluate the dot product F ⋅ dr along the path C:

F(r(t)) ⋅ dr = ⟨5sin(t^3), -4cos(-3t^2), 10t^3(2^t)⟩ ⋅ ⟨3t^2, -6t, 2^t ln(2)⟩ dt

= 15t^2 sin(t^3) + 24t cos(3t^2) + 20t^3 (2^t) ln(2) dt

Finally, we integrate this expression over the interval 0 ≤ t ≤ 1 to get the value of the line integral:

∫CF ⋅ dr = ∫0^1 (15t^2 sin(t^3) + 24t cos(3t^2) + 20t^3 (2^t) ln(2)) dt

This integral cannot be evaluated exactly, but we can use numerical integration to approximate the value. Using a numerical integration tool, the value of the line integral is approximately equal to 11.108.

Therefore:

∫CF ⋅ dr ≈ 11.108

Step-by-step explanation:

The point-slope equation of a line that passes through the points (5, 2) and (-1,-6) include the following: B. y - 2 = 4/3(x - 5).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-6 - 2)/(-1 - 5)

Slope (m) = -8/-6

Slope (m) = 4/3.

At data point (5, 2) and a slope of 4/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 4/3(x - 5)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

In the Venn diagram , the given statement is invalid.

What is Venn diagram?

Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.

Here the given Venn diagram the total number of outstanding endurance contains both Lebron James is triathlete and may be not triathlete. But he does have outstanding endurance.

Hence the given statement is invalid.

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The two companies charge the same when the amount of sugar is 20 thirds per second and the cost when the two companies charge the same is $8,125.

What is amount?

Amount is a term used to describe the quantity or size of something. It can refer to a specific quantity of a substance, such as an amount of money or an amount of a particular material, or it can refer to a more abstract concept, such as an amount of time or effort.

To find the amount of sugar for which the two companies charge the same, we need to set the two costs equal to each other and solve for the amount of sugar.

Let x be the amount of sugar in third per second. Then, the cost C1 charged by the first company is:

C1 = 4500 + 175.25x

And the cost C2 charged by the second company is:

C2 = 3995 + 200.50x

To find the amount of sugar for which the two companies charge the same, we set C1 equal to C2:

4500 + 175.25x = 3995 + 200.50x

Solving for x, we get:

25.25x = 505

x = 20

Therefore, the two companies charge the same when the amount of sugar is 20 thirds per second.

To find the cost when the two companies charge the same, we can substitute x = 20 into either of the cost equations. Let's use C1:

C1 = 4500 + 175.25x

C1 = 4500 + 175.25(20)

C1 = 8125

Therefore, the cost when the two companies charge the same is $8,125.

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Finding the reciprocal of the number -7 gives -1/7

From the question, we have the following parameters that can be used in our computation:

Number = -7

As a general rule, the reciprocal of a number x is 1/x

Using the above as a guide, we have the following:

Reciprocal = -1/7 given that Number = -7

To check, we have

-1/7 * -7

Evaluate

Result = 1

Hence, the reciprocal is 1

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D = 8.3 mm

The radius of the circle is 4.15 mm.

The radius and diameter are both important properties of a circle, and they are related to each other. The diameter is the distance across the circle through its center, while the radius is the distance from the center to any point on the circle. The radius and diameter are related by the formula

D = 2r

Where "D" is the diameter and "r" is the radius.

To calculate the radius of a circle given its diameter, we use the formula

r = D/2

Where "r" is the radius and "D" is the diameter. The formula tells us that the radius is equal to half of the diameter.

In this case, we are given that the diameter is 8.3 mm. To find the radius, we simply substitute this value into the formula and solve for "r"

r = D/2

r = 8.3 mm/2

r = 4.15 mm

Therefore, the radius of the circle is 4.15 mm.

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The only solution that satisfies the original equation is x ≈ 17.465. The other solution, x ≈ 1.535, is an extraneous solution.

How to check the equation has extraneous solutions or not?

We need to check if either of these solutions is an extraneous solution, which means it does not satisfy the original equation.

Here given equation,

√(3x - 5) = x - 8

Here we want to isolate the square root on one side and square both sides.

Squaring both side,

√(3x - 5)² = (x - 8)²

expanding the right side

3x - 5 = x² - 16x + 64

bringing all terms to one side)

x² - 19x + 69 = 0

We are solving this quadratic equation using the quadratic formula,

x = [19 ± √(19²- 4(1)(69))] / (2(1))

x = [19 ± √(253)] / 2

x ≈ 1.535 or x ≈ 17.465

Now, we plug each solution back into the original equation and see if we get a true statement.

Checking x ≈ 1.535:

√(3(1.535) - 5) = 1.535 - 8

√(0.605) ≈ -6.465 (not true)

Checking x ≈ 17.465,

√(3(17.465) - 5) = 17.465 - 8

√49.59 ≈ 9.465 (true)

Therefore, the only solution that satisfies the original equation is x ≈ 17.465. The other solution, x ≈ 1.535, is an extraneous solution.

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ f(x)=5\cdot 3^x\hspace{5em}f(-2)=5\cdot 3^{-2}\implies f(-2)=5\cdot \cfrac{1}{3^2}\implies f(-2)=\cfrac{5}{9}[/tex]

5/9 is closer to 1 than 4/7.

To find out, we can subtract each fraction from 1 and take the absolute value of the result. The fraction with the smaller absolute value is closer to 1.

For 4/7:

1 - 4/7 = 3/7

For 5/9:

1 - 5/9 = 4/9

Since 4/9 is smaller than 3/7, 5/9 is closer to 1.

~~~Harsha~~~

The area of the composite figure that is composed of triangles and a rectangle is: 154 mm².

The composite figure given comprises two different triangles and one rectangle. Therefore, to find the area of the composite figure, we need to calculate the area of each shape in the figure.

Area of rectangle = length * width = (7 + 7) * 4

= 14 * 4

Area of rectangle = 56 mm²

Area of the larger triangle = 1/2 * base * height

= 1/2 * 14 * 11

= 77 mm²

Area of the smaller triangle = 1/2 * 14 * 3

= 21 mm²

Therefore, area of the composite figure = 56 + 77 + 21

= 154 mm²

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Answer:

[tex] \frac{52}{13} = \frac{y}{14} [/tex]

[tex]4 = \frac{y}{14} [/tex]

[tex]y = 56[/tex]

1. Difference between ointment and cream -

Generally, Creams tend to have lighter texture and consistency. They are mostly formulated with a blend of two components, that is water and oil.

Ointments are essentially greasy and have thicker consistency. They contain more oil content as compared to creams. Creams are absorbed faster via the skin than ointments. While ointments are absorbed slower through the skin than creams.

2. The label may instruct you to shake a liquid medicine before using so that the active ingredients are evenly distributed throughout it. The important thing to remember is that you have to shake a suspension before giving each dose so that the medicine particles are evenly distributed throughout the liquid.

3. Emulsions are stabilized by adding an emulsifier or emulsifying agents. These agents have both a hydrophilic and a lipophilic part in their chemical structure. In addition to this protective barrier, emulsifiers stabilize the emulsion by reducing the interfacial tension of the system.

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To test the claim that more than one-third of employers have sent an employee home for inappropriate attire, we can set up the following null and alternative hypotheses:

Null hypothesis: p ≤ 1/3

Alternative hypothesis: p > 1/3

where p is the true proportion of all employers who have sent an employee home for inappropriate attire.

We can use the sample proportion, 964/2765 = 0.349, as an estimate of the true proportion p. To test the hypotheses, we can calculate the test statistic z as:

z = (p - 1/3) / sqrt((1/3)*(2/3)/n)

where n is the sample size (2765).

Plugging in the values, we get:

z = (0.349 - 1/3) / sqrt((1/3)*(2/3)/2765) = 4.28

Using a standard normal distribution table or calculator, the P-value for this test is less than 0.0001 (or approximately 0.0000 when rounded to four decimal places), indicating strong evidence against the null hypothesis.

Therefore, we can reject the null hypothesis and conclude that there is convincing evidence to support the claim that more than one-third of employers have sent an employee home for inappropriate attire.

The equivalent expression using associative property is; 5×(3×12).

Given expression is; [(5 × 3) × 12]

The associative property is a property of addition and multiplication that allows the grouping of numbers or variables without changing the result.

For addition: (a + b)+c = a+(b + c)

For multiplication: (a × b) ×c = a × (b × c)

In simpler terms, it means that you can add or multiply a set of numbers in any order, and still get the same result.

Therefore, the equivalent expression to [(5 × 3) × 12] using only the associative property would have the same operands but a different grouping. One possibility would be;

[(5 × 3) × 12] = [5 × (3 × 12]

Both expressions simplify to 180.

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Note that where the above conditions are given, the probability of A ∩ B is 1/20 and the probability of the union of A  and B P( A∪B) = 2/5. See the explanation below.

We are given that A and B are events that are independent, P(A∩B), we can rightly state that:

P(A∩B ) = P(A) x P (B)

(1/5) x  (1/4)
= 1/20

For P(A∪B)
⇒ P( A ∪B) = P (A ) + P(B) - P(A ∩B)

We can substitute the probabilities to derive:

P(A∪B)  = (1/5) + (1/4) - (120)

We can write the above as:

⇒ 4/20 + 5/20 - 1/20
= 8/20

Simplifying , we get:

P(A∪B)  = 2/5

Hence it is correct to state that the P(A ∩ B) = 1/20, while P(A∪B) = 2/5.

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The maximum profit is given as $31,310

a. In order to determine the intervals in which profitability P increases and decreases, we need to analyze the first derivative of its respective function, P(x).

Given the profit equation: P(x) = 2.36x - (x^2 / 25000) - 3500, the process begins by articulating its derivative, P'(x):

P'(x) = d(2.36x) - d(x^2 / 25000) - d(3500)

P'(x) = 2.36 - (2x / 25000)

P'(x) = 2.36 - x / 12500

Seeing that P'(x) > 0 implies a rising P while P'(x) < 0 portrays a decreasing P, those values must be determined. Subsequently, the critical points may be found by setting P'(x) = 0:

2.36 - x / 12500 = 0

x / 12500 = 2.36

x = 2.36 * 12500

x = 29500

To adequately evaluate the intervals (0, 29500) and (29500, 50000), we must gauge whether P'(x) is positive or negative:

For x greater than zero & less than 29500:

P'(x) = 2.36 - x / 12500 > 0

For x higher than 29500 but falling beneath 50000:

P'(x) = 2.36 - x / 12500 < 0

Hence, P is augmented on the interval from 0 until 29500, whereas it diminishes from 29500 to 50000.

b. Differentiate again the profit function we get

P'(x)= -1/12,500 <0

Therefore the profit will be maximum.

Hence 29500 bags of popcorn must cinema sell in order to maximize profit.

The maximum profit = $31,310

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Answer:

--------------------

Area of the rectangle:

Area of the two triangles:

Area of trapezoid is the sum of the areas we found above:

The matching answer choice is B.

Answer:

d = √ (4 - (-5))² + (-9 - 2)²

d = √ 9² + (-11)²

d = √81 + 121

d = √202

d ≈ 14.21

Therefore, the distance between (-5, 2) and (4, -9) is approximately 14.21 units. The answer is (C) 14.21.

Step-by-step explanation:

leave thanks

Answer:

456

Step-by-step explanation:

This is a mathematical problem that involves exponential decay. To predict the number of African cheetahs living in the wild in 21 years, we need to use the formula:

N(t)=N0​×(1−r)t

where N(t) is the number of cheetahs after t years, N0​ is the initial number of cheetahs, and r is the annual rate of decline.

According to 1, scientists estimate that fewer than 8,000 African cheetahs are living in the wild today and that the population is expected to decline at a rate of 9.8% per year. Therefore, we can plug in these values into the formula:

N(21)=8000×(1−0.098)21

Using a calculator, we can simplify this expression to get:

N(21)≈8000×0.057≈456

Therefore, we can predict that there will be about 456 African cheetahs living in the wild in 21 years, if nothing changes.

This is a very alarming number and shows how endangered these animals are. We need to take urgent action to protect them and their habitats from threats such as habitat loss, human-wildlife conflict, and illegal trade.

It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.

Find the radius of the pool:

Since the diameter is 115 cm, the radius (r) will be half of that:

Radius (r) = Diameter / 2

r = 115 cm / 2

r = 57.5 cm

Calculate the volume of the pool when filled to a depth of 20 cm:

Since the pool is round and assuming it has a cylindrical shape, we can use the formula for the volume of a cylinder:

Volume = π × r² × h

where π (pi) is approximately 3.14159, r is the radius, and h is the height (or depth, in this case).

Volume = 3.14159 × (57.5 cm)² × 20 cm

Evaluate the volume:

Volume ≈ 3.14159 × 3306.25 cm² × 20 cm

Volume ≈ 3.14159 × 66125 cm³

Volume ≈ 207354.2 cm³

Calculate the time it takes to fill the pool to a depth of 20 cm:

We are given that the hose fills the pool at a rate of 34,000 cm³ per minute. To find out how long it will take to fill the pool, we can use the following formula:

Time = Volume / Fill Rate

Time ≈ 207354.2 cm³ / 34,000 cm³/min

Time ≈ 6.1 minutes

It will take approximately 6.1 minutes to fill the pool to a depth of 20 cm at the given fill rate.

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The equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.

The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.

We can use the point-slope form of the equation of a line to find the equation of the line that goes through the point (0, -4) and has a slope of 2.

The point-slope form of the equation of a line is:

y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope of the line.

Plugging in the values, we get:

y - (-4) = 2(x - 0)

Simplifying, we get:

y + 4 = 2x

Subtracting 4 from both sides, we get:

y = 2x - 4

Therefore, the equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.

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