Which point is a solution to the system x2 + y2 ≤ 25 and x < y2 – 2?


(–5, 0)

(–2, 0)

(5, 0)

(2, 2)

(its not c)

Answer:

C

Step-by-step explanation:

The explicit formula is aₙ = -6 · 2⁽ⁿ⁻¹⁾, and we want to find the 9th term in the sequence. To find it, we can simply substitute n = 9 into the explicit formula, which gives us:

a₉ = -6 · 2⁽⁹⁻¹⁾

= -6 · 2⁸

= -6 · 256

= -1536

Hope this helps!

Answer:

Acute

Step-by-step explanation:

c\(c^{2}<a^{2}+b^{2} =Acute\\16^{2}<14^{2}+8^{2} \\252<196+64\\252<260\)

The minimum value is 15, the maximum value is 95, and the median can be found by arranging the data in order and finding the middle value.

To draw a box and whisker plot for the given data: 35, 60, 20, 80, 95, 15, 40, 85, 75, we need to determine the five-number summary, which includes the minimum value, the first quartile, the median, the third quartile, and the maximum value.

The minimum value is 15, the maximum value is 95, and the median can be found by arranging the data in order and finding the middle value. In this case, the median is 60.

To find the first and third quartiles, we need to divide the data into two halves at the median, and then find the median of each half.

The lower half of the data is 15, 20, 35, and 40, with a median of 27.5. The upper half of the data is 75, 80, 85, and 95, with a median of 82.5. Therefore, the first quartile is 27.5 and the third quartile is 82.5.

To draw the box and whisker plot, we start by drawing a number line that includes the range of the data (from 15 to 95).

We then draw a box that spans from the first quartile to the third quartile, with a vertical line inside the box at the median. We draw a horizontal line (whisker) from each end of the box to the minimum and maximum values.

Therefore, the box and whisker plot for the given data is shown below:

lua

Copy code

 10   20   30   40   50   60   70   80   90   100

 |              ------

 |            /        \

 |           /          \

 |        -----         |

 |      /       \       |

 |    /           \     |

 |  15              95 |

The box represents the middle 50% of the data, with the vertical line inside it showing the median. The whiskers show the full range of the data, with any outliers shown as individual points beyond the whiskers. In this case, there are no outliers.

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To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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The area of the polygon is 341.1

We need to find first the base of the triangle

using Pythagorean theorem, a^2+b^2 = c^2

we have the base of 4.18

since the polygon is symmetric and regular, we have 16 same triangles within the polygon

using the area of the triangle multiply by 16 we can get 341.1

Solving for y in terms of x gives y = 31 - 5x

The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.

It is also described as the variable that is being worked out in a given equation.

Given the equation;

5x +y = 31

Let's make 'y' the subject

We have to make 'y' stand alone by taking the other variables or terms over the equality sign, we have

y = 31 - 5x

Thus, solving for y in terms of x gives y = 31 - 5x

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Answer:

2 x ^2 − 2 x + 4 = 0

x ^2 − 2 x + 4 = 0

2 x ^2 − x = 0

Step-by-step explanation:

Answer:

What is the full question?

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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Answer:

Y=5

X=0

Step-by-step explanation:

I dno if it's fully correct tho sorry

Answer: To allocate the two limited-edition wooden chairs efficiently and maximize total economic surplus, we should assign the chairs to the buyers who value them the most, up to the point where the price they are willing to pay equals or exceeds the minimum price of $150.

Given the maximum prices of the potential buyers, we can allocate the chairs as follows:

To calculate the total economic surplus, we sum up the differences between the prices paid and the minimum price for each chair allocated:

Economic surplus = ($150 - $120) + ($150 - $220) = $30 + (-$70) = -$40

The total economic surplus in this allocation is -$40.

Answer:

Height is 0.5

Step-by-step explanation:

height of parallelogram = area ÷ base

= 2.5 ÷ 5 = 0.5

The interquartile range (IQR) is a measure of the spread or variability of the middle 50 percent of the data.

The interquartile range (IQR) is a statistical measure that describes the spread or dispersion of the middle 50 percent of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.

The quartiles divide a dataset into four equal parts, each representing 25 percent of the data. The first quartile (Q1) represents the lower boundary of the middle 50 percent, while the third quartile (Q3) represents the upper boundary of the middle 50 percent. The IQR captures the range of values within this middle range.

By focusing on the middle 50 percent of the data and excluding the extreme values, the interquartile range provides a measure of variability that is less affected by outliers or extreme values. It is commonly used in descriptive statistics and data analysis to understand the spread and distribution of a dataset, particularly when the data is not symmetrically distributed or contains outliers.

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The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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The answer of the given question based on the cylinder is ,  the volume of the solid = 929.44  inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.

Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.

To find volume of  solid, we need to subtract  volume of  inner cylinder from  volume of outer cylinder.

Volume of the outer cylinder = πr²h

where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)

h = height of the outer cylinder = 23 inches

Volume of the outer cylinder = π(4)²(23) = 368π in³

Volume of the inner cylinder = πr²h

where r = radius of the inner cylinder = 2 inches

h = height of the inner cylinder = 18 inches

Volume of the inner cylinder = π(2)²(18) = 72π in³

So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder

= 368π - 72π

= 296π

= 929.44  inch³

The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.

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B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's get the line using 2 points of the graph:

Slope-intercept formula:

So the line is:

The line is solid and shaded area is lower part, therefore the inequality is:

Susan has one gallon of 25% acid solution and needs to know how much pure acid she should add to make it a 75% acid solution.

To solve the problem, we will use the following formula:
(V1 x C1) + (V2 x C2) = V3 x C3
Where:
V1 = Volume of the first solution
C1 = Concentration of the first solution
V2 = Volume of the second solution
C2 = Concentration of the second solution
V3 = Final volume of the mixture
C3 = Final concentration of the mixture
Now, let's plug in the values we know:
V1 = 1 gallon
C1 = 25%
C2 = x (unknown)
V3 = 1 gallon
C3 = 75%
(1 x 0.25) + (x) = (1) (0.75)
0.25 + x = 0.75
x = 0.5
Therefore, Susan needs to add 0.5 gallons of pure acid to her one gallon of 25% acid solution to make a 75% acid solution.

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Answer:

y = 21

Step-by-step explanation:

You need to find k

y = x

54 = 9k  Divide both sides by 9

6 =k

y = 6(3.5)

y = 21

A confidence interval is constructed to estimate the value of a parameter.

In statistics, a parameter refers to a numerical characteristic of a population, such as the population mean or population proportion. When we want to estimate the value of a parameter, we construct a confidence interval.

A confidence interval provides a range of values within which we believe the true parameter value is likely to fall, based on our sample data. It is constructed using sample statistics and takes into account the variability and uncertainty in the estimation process.

A confidence interval is constructed to estimate the value of a parameter, not a statistic.

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The value of the exponential function, f(x), when x = 18 is 14.44

An exponential function is a function that consists of a constant term that has an index of the argument of the function, or in which the argument of the function is an index of a constant.

The general form of an exponential function is presented as follows;

The value of f(0) is left out in the information, therefore, where k = 0, we get;

f(x) = a·bˣ

From the question, we get;

f(4) = 25, therefore;

f(4) = 25 = a·b⁴

f(11) = 19, therefore;

f(11) = 19 = a·b¹¹

f(4)/f(11) = 25/19 = a·b⁴/(a·b¹¹) = b⁻⁷

b⁷ = 19/25

b¹⁸ = b⁷⁺¹¹ = b⁷ × b¹¹

b¹¹ = 19/a

f(18) = a·b¹⁸ = a × b⁷ × b¹¹ = a × b⁷ × b¹¹ = a × (19/25) × 19/a = 19²/25

f(18) = 19²/25

f(18) = 361/25 = 14,44

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Answer:

the percentage profit is 20%

Step-by-step explanation:

Given that

Sean paid  £10 for 24 chocolate bars

He sold all 24 chocolate bars for 50p each

we need to find out the percentage profit

Since he paid  £10 and sale value is (24 × 0.50) i.e. £12

So, the percentage profit is

= (£12 - £10) ÷ (£10)

= 20%

Hence, the percentage profit is 20%

Answer:

devide 1080 by 5 and 2880 by 5 the it will 216 and 576

Answer: 1080 is an. Octagon, 8 sides

180 is a triangle.

2880 is an 18gon 18 sides

Step-by-step explanation:

Divide the sum of the interior angles by 180 and add 2 to the dividend.

1080/180=>6+2=8

180/180 => 1 +2 =3

2880/180=> 16+2= 18

Answer:

Step-by-step explanation:

As per diagram we have

DG = GW (congruent as corresponding sides)

m∠DGF = m∠WGF = 90°

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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Explanation:

Factoring to linear factors generally involves finding the roots of the polynomial.

The two rules that are taught in Algebra courses for finding real roots of polynomials are ...

In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.

Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)

__

Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.

There are web apps that will find all roots of virtually any polynomial of interest.

_____

Additional comment

Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.

what is the question your trying to find, if you could repile to this so I can try to figure it out. (I'll be heading off soon)

The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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