a circle is divided into 4 sectors, the ratio of whose areas is what is the central angle of the largest sector in degrees?

The solution to the given inequality  [tex]-5f + 6 > 10f - 10[/tex] is [tex]f < 16/15[/tex].

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

[tex]-5f + 6 > 10f - 10[/tex]

To solve the inequality [tex]-5f + 6 > 10f - 10[/tex], we need to isolate the variable [tex]f[/tex] on one side of the inequality.

We will first subtract 6 from both sides to isolate the [tex]-5f[/tex] term:

[tex]-5f + 6 - 6 > 10f - 10 - 6[/tex]

Simplifying the left side:

[tex]-5f > 10f - 16[/tex]

Next, we will subtract [tex]4f[/tex] from both sides to isolate the [tex]-5f[/tex] term on the left side:

[tex]-5f - 10f > 10f - 10f - 16\\-15f > -16[/tex]

Finally, we will divide both sides by -9,

[tex]-( 15 f )/9 > -16/15[/tex]

Dividing both sides by -15:

[tex]f < 16/15[/tex]

This is the required solution to the given inequality.

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Answer:

6.00

Step-by-step explanation:

4r + g = 24

4r + 2g = 30       Subtract equation 2 from equation 1

     -g = -6

so g = cost of gravity = 6 dollars

Answer:

(-2,2)

Step-by-step explanation:

First, let's look at the 2 inequalities:

y ≤ -x + 1

y > x

Just by looking at the second inequality, we can remove any ordered pairs where x is greater than or equal to y. This eliminated the ordered pairs (-1,-3) and (0,-1). Now, the answer has to be (-3,5) or (-2,2). Knowing this, we can plug x and y into the equation and see if either of the answers are true.

(-3,5):

x = -3

y = 5

y ≤ -x + 1

5 ≤ -(-3) + 1

5 ≤ 3 + 1

5 ≤ 4

NOT TRUE

(-2,2)

x = -2

y = 2

2 ≤ -(-2) + 1

2 ≤ 2 + 1

2 ≤ 3

TRUE

So, since plugging in the ordered pair (-2,2) into the inequality gives us a true answer while (-3,5) doesn't, the order pair (-2,2) must be out answer.

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The system of equations graphically on the set of axes is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

y = (1/6)x + 7

y = -2x - 6

The graph of each equation is given below.

The point of intersection is (-6, 6).

i.e,

(1/6)x + 7 = -2x - 6

(1/6)x + 2x = -6 - 7

13x/6 = -13

x/6 = -1

x = -6

So,

y = -2x - 6

y = -2 x -6 - 6

y = 12 - 6

y = 6

Thus,

The system of equations graphically is given above.

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The gross pay of the worker when using the given parameters is; $1,129.46

Gross pay is defined as the total amount of money you get before taxes or any other deductions are subtracted from your salary.

Net pay is defined as the amount of pay remaining for issuance to an employee after deductions have been taken from individual's gross pay.

Thus;

Gross pay = Net pay + deductions

Net pay = Gross pay - deductions

The parameters are;

Regular salary: $984 per month

Overtime rate: $10.39 per hour (14 hours overtime to be paid)

Gross Pay = 984 + 14(10.39)

Gross Pay = $1,129.46

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Answer:

A=2

B=2+3÷2=2.5

C=10+15÷2=12.5

D=20

The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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The variable b in terms of the variables a and c is b = ac/(a - c)

From the given formula expressed as

1/a + 1/b = 1/c

We want to express variable b in terms of the variables a and c. We would make variable b the subject of the formula.

Subtracting 1/a from the left hand side of the equation and the right hand side of the equation, it becomes

1/a - 1/a + 1/b = 1/c - 1/a

1/b = 1/c - 1/a

1/b = (a - c)/ac

Taking the reciprocal of the left hand side of the equation and the right hand side of the equation, it becomes

b = ac/(a - c)

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The volume of one carton of strawberries is 200 in³.

The volume of all of the cartons of strawberries is 6,000 in³.

The volume of each carton can be determined by multiplying the length, width and height together.

Volume = length x width x height

10 x 4 x 5 = 200 in³

The volume of all the boxes of strawberries can be determined by multiplying the number of cartons by the volume of one carton.

Volume of the 30 cartons of strawberries = 200 in³ x 30 = 6,000 in³

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The length of the diagonal is 12.6 feet.

"Information available from the question"

The perimeter of a rectangle is 32 feet.

The length is three times as long as the width.

We have to find the length of the diagonal.

Let w = width

then

3w = length.

Because we know the perimeter:

Perimeter of the rectangle is : 2(l + w)

32 = 2(w + 3w)

32 = 2(4w)

16 = 4w

4 feet = w (width)

Length:

3w = 3(4) = 12 feet

Diagonal, we use the Pythagorean theorem:

Let d = diagonal

then,

[tex]d^2 = 4^2 + 12^2[/tex]

[tex]d^2[/tex] = 16 + 144

[tex]d^2[/tex] = 160

d = 12.6 feet

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The correlation between the two variables in the data set for 13 colonies of sparrowhawks is 0.5602.

This means that there is a moderate positive correlation between the two variables, indicating that when one variable increases, the other variable is likely to increase as well.

To calculate the correlation coefficient, we can use Pearson’s correlation coefficient equation:

r = (n * Σxiyi - Σxi * Σyi) / √[(n * Σxi2 - (Σxi)2) * (n * Σyi2 - (Σyi)2)]

Where: n = the number of observations Σxi = the sum of all x-values Σyi = the sum of all y-values Σxiyi = the sum of the products of each x-value and y-value Σxi2 = the sum of the squares of each x-value Σyi2 = the sum of the squares of each y-value

Plugging in the values for our data set, we get:

r = (13 * 0.5602 - (13 * 0.5602)) / √[(13 * 0.2532 - (13)2) * (13 * 0.2532 - (13)2)]

r = 0.5602

This means that there is a moderate positive correlation between the two variables in the data set, indicating that when one variable increases, the other variable is likely to increase as well.

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In a residual plot, the residuals are plotted against the predictor variable. Ideally, the residuals should be randomly scattered around zero, without any patterns or trends.

If there is a pattern, it suggests that the linear model is not an adequate representation of the data and a more complex model may be necessary.

In this case, the residual scatter plot shows that the residuals are randomly scattered around zero, which suggests that a linear model is appropriate for summarizing the relationship between the predictor and response variables. This means that a straight line can be used to approximate the relationship and make predictions based on the data.

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Answer:

250

Step-by-step explanation:

190 students = 76%

190/76=2.5

2.5 x 100 =250

Answer:

Slope: y= 4/5x+21/8

The distance is 4 units up and 5 units to the right.

Step-by-step explanation:

Answer:

12w+19

Step-by-step explanation:

[tex]3(4w + 2) + 13[/tex]

[tex]3(4w) + 3(2) + 13[/tex]

[tex]12w + 6 + 13[/tex]

[tex]12w + 19[/tex]

12suitcase

Answer: 4

Step-by-step explanation:

(-88) - (-44) = -36

remove the (-) = 36

36 ÷ 9 = 4

Answer:

assuming that it can be solved, then yes

Step-by-step explanation:

Answer: 900

Step-by-step explanation:

The Interior Angle formula is (n-2)x180. So you take 7 minus 2 times 180 and that gives you 900

Answer3rd one and 1st

Step-by-step explanation:

If a man has a garden and he divide them equally into minimum number of square plots , then length of each square plot is 28m  .

the length of the garden is = 84m  ;

the width of garden is = 56m ;

the man is dividing the garden into equally minimum number of square plots ,

then , Factors of Width = 2×2×2×2×7 = 2×28  ;

the Factors of Length is = 2×2×2×3×7 = 3×28  ;

So , we will notice with a side of 28 m each , we can make 2 squares along the width of the garden ;

Similarly , with the side = 28m each, we can make 3 squares along the length of the garden ;

That means , we can make 6 squares of 28m side.

Therefore , the minimum length of each square plot = 28 m.

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The probability that a tire of this brand will last longer than 58,000 miles is  0.8413 or 84.13%.

Given in the question that the tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2000 miles.

We have to calculate the probability that a particular tire of this brand which will last longer than 58,000 miles.

The standard normal variable corresponding to the given tire's tread life being longer than 58,000 miles can be calculated using the z-score formula:

The formula for computing a z-score is =(DataValue-Mean)/StDev

Therefore , we can write z = (58,000 - 60,000) / 2000

Hence, z = -1

Next, we can use a standard normal table to find the probability that a standard normal variable will be less than -1:

P(Z < -1) = 0.1587

Hence P = 1 - 0.1587

            P = 0.8413

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To create a scale illustration of her bedroom, Elena must draw a 10cm by 6cm rectangle.

To create a scale illustration of her bedroom she must take into account the scale she will be using. In this case it would be 1:50, that is, each original unit must be divided into 50 parts. Therefore, we must divide the lengths into 50 as shown below. Additionally we must take the values in cm.

According to the above, a scale model would be 10cm by 6cm.

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The simplification steps are as follows:

(2³)(7.2³) = 2³+3 = 128

(5³)³ = 125

(1 + 3) = 4

72² = 5184

125 - 7 = 118

So, the simplified expression is:

118 (5xy³) (5184³) 2y

Properties of rational exponents are rules that dictate how to simplify expressions with fractional exponents. Some of the key properties are:

Fractional Exponent: a^(m/n) = (a^m)^(1/n)

These properties are used to simplify expressions with rational exponents, which are exponents that are in the form of a fraction.

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The water's height at 8:30 PM is approximately 0.69 feet.

As per the data given in the question,

We have the equation,

depth = 4 * sin (0.5 * t)

where t is the number of hours after midnight.

As we need to find the depth of the water at 8:30 PM,

For finding the value of the depth at 8:30 PM we need to first convert 8:30 PM to the number of hours after midnight.

8:30 PM = 20.5 hours after midnight

So, substituting t = 20.5 into the equation,

we will get it as:

depth = 4 * sin (0.5 * 20.5)

depth = 4 * sin (10.25)

depth = 4 * 0.1736481776669303

depth = 0.6945971520676809

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Answer:

B.

Step-by-step explanation:

i think 99.9% sure!

Answer:

he representation that is most appropriate to show the relationship between the number of chapters and the total pages of a book is given by:

Graph 3

How to choose the correct graph?

Before choosing the correct graph, we must classify the function as discrete or continuous, as follows:

Discrete function: the input values of the function are only certain values on an interval.

Continuous function: the input values of the function are all the real values in the interval.

Then the graph of each type of function is given as follows:

Discrete function: dots.

Continuous function: solid line.

The input and output variables in this problem are given as follows:

Input variable: number of chapters.

Output variable: number of pages.

The number of chapters assumes only integer values, hence the function has a discrete domain, meaning that the graph is composed by dots.

However, the first graph is correct, as the third graph has a range of input and output values that is not present on the table, while the range in the first graph is according to the table.

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Step-by-step explanation: