What mathematical statement calculates a value?

Answer:

Step-by-step explanation:

The correct answer from options are,

a) x⁴ – 6x²  – 27 = 0,

d) 6(2x + 4)² = (2x + 4) + 2  and,

e) 6x⁴ = -x² + 5.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must contain at least one term of the second degree.

Given equations to find the  equations that are quadratic in form,

Standard form refers to the quadratic function f(x) = a(x - h)² + k, where a is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.

so equations that are in form of quadratic are,

x⁴ – 6x²  – 27 = 0,

6(2x + 4)² = (2x + 4) + 2,

6x⁴ = -x² + 5

and rest all other equations are not in form of quadratic.

Hence options A, D, and E are correct.

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The average amount of cliff's height that decreased each year is 1/6 inches.

The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -

{ r } = y/x                                                          .... Eq { 1 }

Given is that over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project.

We can write the the average amount of cliff's height that changed each year as -

{r} = |h|/|t|

{r} = 3/18

{r} = 1/6

Therefore, the average amount of cliff's height that decreased each year is 1/6 inches.

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The probability of rolling 3 sixes to the nearest thousandth is 0.556.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Using binomial distribution.

[tex]^nC_r P^cQ^{n - r}[/tex]

Now,

Probability of getting a six = 1/6

P = 1/6

Probability of not getting a six = 5/6

Q = 5/6

Now,

n = 5 and r = 3

So,

[tex]^nC_r P^rQ^{n - r}[/tex]

= [tex]^5C_3(1/2)^3(5/6)^2[/tex]

= (5 x 4)/2 x (1/2) x (1/2) x (1/2) x (5/6) x (5/6)

= 10 x 1/8 x 25/36

= 5/9

= 0.556

Thus,

The probability of rolling 3 sixes is 0.556.

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Answer:

Step-by-step explanation:

0.10267857142000002

The value of ST = 10 for the given rectangle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

In the given triangle PQRS, the diagonals bisect each other, that is they divide each other in equal halves.

Thus. PT = TR

Since, PT = 10 we have TR = 10,

The diagonals of the rectangle are equal, hence we also have:

TR = ST

Since, the value of TR = 10, then the value of ST = 10.

Hence, the value of ST = 10 for the given rectangle.

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Answer:

  CG = 8

Step-by-step explanation:

Given CG = 4x-16 is congruent to AG = 2x -4, you want the value of CG.

The congruent segments are equal length:

  CG = AG

  4x -16 = 2x -4

  2x = 12 . . . . . . . . . . add 16 -2x

Substitute into the expression for AG:

  2x -4 = 12 -4 = 8

AG is congruent to CG, so ...

  CG = 8

__

Additional comment

You know triangles GBC and GBA are congruent by the HA theorem, since GB bisects angle ABG. Corresponding parts of congruent triangles are congruent, so CG ≅ AG.

The relation between a and c can be written as:

a = c + 24

First we know two equations:

a = b + 12

b = c + 12

So we have relations between a and b, and between b and c, and we want a relation between a and c.

If we replace the b of the first equation with the second equation, then we will get:

a = (c + 12) + 12

a = c + 24

That is the relation between a and c.

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The approximate lateral area of the cone is equal to 200.96 cm².

Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:

Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)

Where

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circular base = πr²

16π = πr²

Radius, r = √16

Radius, r = 4 cm.

Substituting the given parameters into the lateral area of a cone formula, we have the following;

Lateral surface area of a cone, LSA = πrl = πr4(r)

Lateral surface area of a cone, LSA = 3.14 × 4 × 16

Lateral surface area of a cone, LSA = 200.96 cm².

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Answer:

201 beause you are rounding to the nearest whole number

Step-by-step explanation:

The final account balance with compound interest is $6,440.30.

The final account balance when compounded semiannually is higher.

The formula for compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the future value of the investment, including interest

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested/borrowed for

Part A:

r = 3.92% = 0.0392, P =  $5,460.75, n = 2 (semiannually means twice a year), t = 51 months = 4.25 years

A = P (1 + r/n)^(nt)

A = 5,460.75 (1 + 0.0392/2)^(2*4.25)

A = 5,460.75 (1 .0196)^(8.5)

A = $6,440.30

Thus, the final account balance is $6,440.30

Part B:

difference = 6,440.30 - $5,460.75 = $975.55

When the initial deposit is invested with interest compounded semiannually, the final account balance is higher.

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1km would be represented by 4cm on a  1 : 25000 scale map.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The scale on a 1 : 50000 ordnance survey map indicates that 2cm on the map = 1km on the ground.

We know 1 km = 1×100000 = 100000 cm.

So, If 2 cm represents 100000 cm it has a scale factor of 100000/2 = 50000.

Now, Again 1 km = 100000 cm,

So, 1km will be represented by 100000/25000 = 4 cm.

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The approximate lateral area of the cone is equal to 314 cm².

Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:

Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)

Where

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circular base = πr²

25π = πr²

Radius, r = √25

Radius, r = 5 cm.

Substituting the given parameters into the lateral area of a cone formula, we have the following;

Lateral surface area of a cone, LSA = πrl = πr4(r)

Lateral surface area of a cone, LSA = 3.14 × 5 × 20

Lateral surface area of a cone, LSA = 314 cm².

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Answer:

[tex]10^{7}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

10² × [tex]10^{5}[/tex] = [tex]10^{(2+5)}[/tex] = [tex]10^{7}[/tex]

Answer:

[tex]10^{7}[/tex]

Step-by-step explanation:

[tex]10^{2}*10^{5}=10^{2+5}=10^{7}[/tex]

Answer:bro chilll

Step-by-step explanation:

Answer:pls brainliest :D

Step-by-step explanation:

To find the average daily balance for January, we need to find the total balance for the month and divide by the number of days in the month.

Starting balance: $700

Sofa purchase: $1100

Payment on January 14th: $550

Lamps and household items purchase: $475

Total balance: $700 + $1100 + $475 - $550 = $1825

There are 31 days in January, so the average daily balance is: $1825 / 31 = $58.87.

were going to need a lil more than that to answer :(

Answer:

40 grams

Step-by-step explanation:

Answer: 120-x

Step-by-step explanation:

Answer: 79

Step-by-step explanation: The weighted average for the scores can be calculated as follows:

Lab score: 94 x 0.23 = 21.62

First major test: 89 x 0.215 = 19.135

Second major test: 63 x 0.215 = 13.495

Final exam: 73 x 0.34 = 24.82

Total weighted average: 21.62 + 19.135 + 13.495 + 24.82 = 78.976

Rounding to the nearest whole number, the weighted average is 79.

According to the information in the table, the correct options are: The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A. (option B).

To identify the correct option that matches the information in the survey table, we must read each of the options and compare it with the information in the table to establish one as true.

Based on the above, we can infer that the correct option is option B because the number of employees who voted for coffee in group B is greater than the number of employees who voted for coffee in group A.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Options:

A. The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.

B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.

C. The estimates for both groups show an equal number of employees would have voted for coffee.

D. The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.

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Answer:

Step-by-step explanation:

Notebooks       Total Cost

0                         0.00

1                          3.00

2                         6.00

3                         9.00

Answer:

see explanation

Step-by-step explanation:

given the ratio of 2 similar figures is [tex]\frac{a}{b}[/tex]

then the ratio of perimeters is also [tex]\frac{a}{b}[/tex]

and the ratio of areas is ( [tex]\frac{a}{b}[/tex] )² = [tex]\frac{a^2}{b^2}[/tex]

the ratio of side lengths, yellow to green is

[tex]\frac{36}{60}[/tex] = [tex]\frac{3}{5}[/tex] ( cancelling 36 and 60 by 12 )

the ratio of perimeters is equal to ratio of sides, that is [tex]\frac{3}{5}[/tex]

the ratio of areas = [tex]\frac{3^2}{5^2}[/tex] = [tex]\frac{9}{25}[/tex]

let x be the area of the green figure, then by proportion

[tex]\frac{45}{x}[/tex] = [tex]\frac{9}{25}[/tex] ( cross- multiply )

9x = 1125 ( divide both sides by 9 )

x = 125

that is the area of the green figure is 125 units²

Answer:

(- 9, 10 )

Step-by-step explanation:

Solve the equations simultaneously to find solution to both

- 6x + 3y = 84 → (1)

- 6x - 3y = 24 → (2)

add (1) and (2) term by term to eliminate y

- 12x + 0 = 108

- 12x = 108 ( divide both sides by - 12 )

x = - 9

substitute x = - 9 into either of the 2 equations and solve for y

substituting into (1)

- 6(- 9) + 3y = 84

54 + 3y = 84 ( subtract 54 from both sides )

3y = 30 ( divide both sides by 3 )

y = 10

solution is (- 9, 10 )

The inequalities representing the graph are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

First, we have to determine the two lines.

Line₁.

(0, 2) and (1, - 1).

m = (- 1 - 2)/(1 - 0).

m = - 3.

- 1 = - 3(1) + b.

b = 2.

y = - 3x + 2.

Line₂.

(0, - 2) and (3, 0).

m = (0 + 2)/(3 - 0).

m = 2/3.

0 = (2/3)(3) + b.

b = - 1.

y = (2/3)x - 1.

So, The two inequalities are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

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Answer:

4

7 * 4 = 28

28 + 2 = 30

Step-by-step explanation:

Hope it helps! =D

Solution is in the attachment!!

Answer: 13 ducklings 5 male 7 female so the answer is 5:7

Step-by-step explanation:

On solving the provided question we cans ay that area of bulletin  board would be 22*10 = 220 cm sq.

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

This question depends on how thick you would want the border to be.

One simple way to find this is finding the perimeter of the bulletin board. You can do this by using the formula: 2(L) + 2(W)

(L) Represents Length

(W) Represents Width

In this situation, it would be 2(4) + 2(6)

that would turn into 8 + 12

which turns into 20 feet.

area of bulletin  board would be 22*10 = 220 cm sq.

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Answer:5 star would be greatly aprreciated

For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:

Max HR = 220 - Age

Since the person is 20 years old, the maximum heart rate can be estimated as:

Max HR = 220 - 20 = 200 beats per minute.

To estimate the maximum heart rate given a resting heart rate, we can use the formula:

Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR

Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:

Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute

Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute

Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute

Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute

For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.

Step-by-step explanation:

For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:

Max HR = 220 - Age

Since the person is 20 years old, the maximum heart rate can be estimated as:

Max HR = 220 - 20 = 200 beats per minute.

To estimate the maximum heart rate given a resting heart rate, we can use the formula:

Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR

Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:

Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute

Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute

Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute

Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute

For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.

To model the data with a linear function, find the slope using two points from the table, and use the slope-intercept form of the equation to find the y-intercept. To estimate the maximum heart rate for different resting heart rates, substitute the values into the equation. The correlation coefficient cannot be determined based on the given table of data.

To model the data with a linear function, we can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope (m). The slope is given by the formula: m = (y2 - y1) / (x2 - x1). We can choose any two points from the table to calculate the slope. Let's choose (60, 200) and (70, 180) as our two points.

Using the formula, we have m = (180 - 200) / (70 - 60) = -20 / 10 = -2.

Now, we can use the slope-intercept form of the equation to find the y-intercept (b). Let's substitute one of the points into the equation: 200 = -2(60) + b. Solving for b, we get b = 320.

Therefore, the equation of the linear function that models the data is y = -2x + 320.

To estimate the maximum heart rate for different resting heart rates, we can substitute the given values into the equation:

If the resting heart rate is 40: y = -2(40) + 320 = 240.

If the resting heart rate is 60: y = -2(60) + 320 = 200.

If the resting heart rate is 72: y = -2(72) + 320 = 176.

If the resting heart rate is 80: y = -2(80) + 320 = 160.

The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, it represents the correlation between resting heart rate and maximum heart rate. The closer the correlation coefficient is to 1 or -1, the stronger the correlation. However, since we are given a table of data and not actual data points, we cannot calculate the correlation coefficient. We can only estimate it visually based on the scatter plot of the data points.

Therefore, the correlation coefficient cannot be determined and our confidence in using the regression line to estimate function values is limited.

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The intervals where the function is decreasing are:

(-3, -1) and (4, ∞)

The function is decreasing when, reading from left to right, the graph goes dondwards.

Now let's find the intervals where that happens.

First that happens between x = -3 and x = 1

And then the function starts decreasing again at x = 4 and keeps decreasing.

Then the intervals where the function decreases are:

(-3, -1) and (4, ∞)

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The rate of change of the height is approximately -1.67 meters per minute.

The volume of a cone can be written as V = (1/3)πr²h.

Differentiating with respect to time t, we get

dV/dt = (1/3)π (2rh dr/dt + r² dh/dt)

Given that the radius is decreasing at a constant rate of 1 meter per minute and the volume is decreasing at a rate of 61 cubic meters per minute, we can substitute these values into the equation to find dh/dt:

61 = (1/3)π (2rh + r² dh/dt)

dh/dt = (61 - (2rh)) / (r² * (1/3)π)

Substituting in the given values of r = 2 meters and h = 41 cubic meters, we get:

dh/dt = (61 - (2 * 2 * 41)) / (2² * (1/3)π)

dh/dt = (61 - 164) / (4 * (1/3)π)

dh/dt = -103 / (4 * (1/3)π)

Approximating π to 3.14, we get

dh/dt = -103 / (4 * (1/3) * 3.14)

dh/dt ≈ -1.67

So the rate of change of the height is approximately -1.67 meters per minute.

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