25. In a company, 40% of the employees are women. The ratio of the number of single women to the number of married women is 2:5. If there are 30 married women how many employees are there in this company?

(Only accurate answers)​

Answer:

Step-by-step explanation:

125.

Answer:

Are we supposed to give the answer in fractions?

The vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).

What is the quadratic function?

A quadratic function is a function of the form [tex]f(x) = ax^2 + bx + c,[/tex] where a, b, and c are constants, and a is not equal to 0. It is a type of polynomial function that can be graphed as a parabola, which is a symmetric curve that opens either upwards or downwards.

Given the table of points for the continuous quadratic function h(x), we can find the vertex and range of the function. Since the function is quadratic and continuous, it can be represented in the standard form [tex]f(x) = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola.

To find the vertex, we can use the fact that the x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively. In this case, a = 1 (since the function is continuous and quadratic), and b can be found using any two points on the parabola:

[tex]b = (h(x2) - h(x1))/(x2 - x1) = (4 - 7)/(-2 + 1) = 3[/tex]

Therefore, the x-coordinate of the vertex is x = -b/2a = -3/2. To find the y-coordinate of the vertex, we can evaluate the function at this value of x:

[tex]h(-3/2) = (1)(-3/2 - h)^2 + k[/tex]

To solve for k, we can use one of the points on the parabola, say (-6, 12):

[tex]12 = (1)(-6 - h)^2 + k[/tex]

Expanding and simplifying, we get:

[tex]12 = (h - 6)^2 + k[/tex]

Substituting -3/2 for h, we get:

[tex]12 = (-(3/2) - 6)^2 + k\\\\12 = 81/4 + k\\\\k = -21/4[/tex]

Therefore, the vertex of the parabola is at the point (-3/2, -21/4).

To find the range of the function, we can look at the shape of the parabola. Since the coefficient of the quadratic term is positive, the parabola opens upwards, and the vertex is the lowest point on the graph. Therefore, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -21/4. In interval notation, we can write the range as (-21/4, infinity).

Hence, the vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).

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The value of x from the adjoining figure​ given as pentagon is 85°.

An angle is a geometric figure formed by two rays, or lines, that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees, radians, or other units of angular measurement, and it represents the amount of rotation between the two rays. Angles are often used in geometry, trigonometry, physics, and other fields to describe the orientation of objects and the relationships between them. Some common types of angles include acute angles (less than 90°), obtuse angles (greater than 90°), and right angles (exactly 90°).

Here,

This is a pentagon with sum of angle as 540 degrees.

50+x=180

x=130°

x+80+120+125+130=540

x=540-455

x=85°

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The surface area of the rectangular prism, found by summing the surface areas of the six rectangular faces is about 2,600 square inches

A rectangular prism is a three dimensional solid with six rectangular faces, such that faces of the prism that face each other are parallel and congruent.

The surface area of the rectangular prism is the sum of the surface areas of the six rectangular faces of the prism

The area of the rectangles that make up the surface are;

A₁ = 8 inches × 36 inches = 288 square inches

A₂ = 23 inches × 8 inches = 184 square inches

A₃ = 23 inches × 36 inches = 828 square inches

A₄ = 23 inches × 8 inches = 184 square inches

A₅ = 8 inches × 36 inches = 288 square inches

A₆ = 23 inches × 36 inches = 828 square inches

The surface area of the rectangular prism, A, is therefore;

A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆

Therefore;

A = 288 + 184 + 828 + 184 + 288 + 828 = 2600

The surface area of the rectangular prism is 2,600 square inches

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The required generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Therefore, option B is the correct.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Given that, a wildlife biologist captured and released 34 trout's from two different lakes and measured them to the nearest inch.

Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.

In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.

Therefore, option B is the correct.

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Answer:

[tex]A. \;x^2 -7x + 1[/tex]

[tex]B.\;5x^2 + 2x[/tex]

Step-by-step explanation:

Standard Form of Polynomial
Standard form of a polynomial is written in the descending order of the power of the variable.

The standard form of polynomial is given by

[tex]f(x) = a_nx^n + a_{n-1}x^{n-1}+....... + a_1x + a_0[/tex]
where [tex]x[/tex] is the variable and [tex]a_i,\; i = 0...n[/tex] are coefficients.

The only two expressions in standard form are
[tex]A. \;x^2 -7x + 1[/tex]

and
[tex]B.\;5x^2 + 2x[/tex] (here the constant a₀ is 0)

The solution is, the average cost of nuts is $15.02.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

from the given information we get,

cost of 9 pound b.nuts = $11.99 *9

cost of 13 pound m.nuts = $17.99 *13

cost of 11 pound p.nuts = $13.99 *11

so, total cost = 107.91 + 233.87 + 153.89

                     =495.67

i.e. average cost = 495.67 / 33

                            =15.02

Hence, The solution is, the average cost of nuts is $15.02.

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The mathematical model that can be used to express the verbal statement of the proportional relationships are;

10. y = k/x²

11. P = k/V

12. P = k·V·I

A proportional relationship is one in which the output variable is a multiple of the input variable and a constant (the constant of proportionality).

10. The verbal statement is; y varies inversely as the square of x

The inverse relationship indicates that a variable is related to the reciprocal of the other variable, therefore;

The mathematical model for the statement can be presented as follows;

y ∝ 1/x²

The constant of proportionality k can therefore be applied as follows;

11. The verbal statement is; For a constant temperature, the pressure P of a gas is inversely proportional to the volume V of the gas

The mathematical model of the proportional relationship is; P ∝ 1/V

Therefore;

12. The verbal statement is; The electric power P of a direct current circuit is jointly proportional to the voltage V and the electric current I

The mathematical model is therefore;

P ∝ V·I

Therefore;

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Using Integration, we can find out that all the fish in the lake died after 20 weeks.

Integration is the process of connecting the parts to create the whole. In the integral calculus, we find a function whose derivative is known. Integration is therefore the opposite of distinction. Integration is used to define and calculate the area enclosed by the function graph. The basic calculus methods used to address arithmetic issues are differentiation and integration.

We first determine the growth rate of the fish, let it be D.

The death rate factor S is to be multiplied by P to get the death rate, so the term is:

- SP = - k P/√P

      = - k√P

Given, birth rate, S is 0.

P' = -k√P

Now, we can separate and integrate it:

P'/√P = -k

∫dP'/√P = ∫-k dt

2√P = -kt + c

Applying the data that we have:

P (0) = 900

2 (30) = 0 + c

⇒ c = 60.

At t = 6,

P = 441

  = (21) ²

So, 2(21) = 60 - 6k

⇒ 6k = 18

⇒ k = 3.

Finally, we set t = 0 and we solve it for t:

2(0) = 60 - 3t

⇒ t = 20.

Therefore, the fish in the lake died after 20 weeks.

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The slope of line A is 6 and the slope of line B is 2

Line A is greater than the slope of line B

A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.

The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.

Therefore, option B is the correct answer.

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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.

The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.

Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

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The composite function has its value to be 54168

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

f(x)=10x^2-8x

g(x)=7x-3.

Given the composite function [f o g] (11)., we have

[f o g] (11) = f(g(11))

Substitute the known values in the above equation, so, we have the following representation

g(11) =7 * 11 - 3

Evaluate

g(11) =74

So, we have

[f o g] (11) = f(74)

[f o g] (11) = 10(74)^2 - 8(74)

[f o g] (11) = 54168

Hence, the solution is 54168

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Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

1) a=4 and b=8

2) Let geometric mean is g. [tex]g=\sqrt ab[/tex] or you can do [tex]g=\sqrt 4 times8[/tex]

3) g=[tex]4\sqrt2[/tex]

Answer:

B. 10 yd., 14 yd., 17 yd.

Step-by-step explanation:

In a right triangle, the squares of the sums of the two shorter sides must equal the square of the longer side(which is the hypotenuse)

From the combinations given only the set 10 yd, 14 yd. and 17 yd does not obey this rule

10² + 14² = 296
17² = 298
So this does not match

The probability that both adults think most celebrities are good role models is  0.046

Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Given that the probability that the celebrities are good role models is 192/900

Then if we pick two adults without replacement; 192/900 * 192/899

= 0.046

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Missing parts;

In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.Find the probability that both adults think most celebrities are good role models.

Answer:

Step-by-step explanation:

Given AB = AC = BC (all sides of equilateral triangle are equal)

BC = 6y + 4

AD = 4y

as D is midpoint of AB, so AB = 2 x 4y = 8y

Since AB = BC

Hence, 8y = 6y + 24

Or, 8y - 6y = 24

Or, 2y = 24

Or, y = 24/2 = 12

Now, Angle ACB = 60 degree (all angles of an equilateral triangle measure 60 degree)

And CD being bisector of side opposite C so it is angular bisector of angle ACB

So, angle ACD = 1/2 of angle ACB

Or, 4x + 2 = 30

Or, 4x = 30 - 2 = 28

Or, x = 28/4 = 7 degree

Answer:

Correct options are A) , B) and D)

A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side.

Answer:

-4

Step-by-step explanation:

-5 x -12/ 3 x -5

60/-15

-4

Using linear programing and graphical method, the solutions are (0, 4), (3, 0) and (6, 4)

To solve the system of inequalities using linear programming, we need to graph the feasible region and find the optimal solution.

First, we will graph the boundary lines of the inequalities. To do this, we will find the x and y intercepts of each line and plot the points. Then we will draw the lines that connect the points.

For the first inequality, 6x - 4y ≤ 18, we can find the x intercept by setting y = 0:

6x - 4(0) = 18

6x = 18

x = 3

For the y intercept, we set x = 0:

6(0) - 4y = 18

-4y = 18

y = -4.5

So the x and y intercepts are (3, 0) and (0, -4.5), respectively.

For the second inequality, -2x + 7y ≤ 28, we can find the x intercept by setting y = 0:

-2x + 7(0) = 28

-2x = 28

x = -14

For the y intercept, we set x = 0:

-2(0) + 7y = 28

7y = 28

y = 4

So the x and y intercepts are (-14, 0) and (0, 4), respectively.

Next, we need to shade the feasible region that satisfies all the inequalities. The feasible region is the region that is below the first line (6x - 4y = 18) and to the left of the second line (-2x + 7y = 28), and in the first quadrant where x and y are both non-negative.

The optimal solution is the point within the feasible region that maximizes the objective function. Since we don't have an objective function to maximize or minimize, we can simply find the corner points of the feasible region and evaluate them to see which one satisfies the original inequalities. The corner points of the feasible region are the intersection points of the boundary lines. In this case, the corner points are (0, 4), (3, 0), and (6, 4).

Evaluating each corner point in the original inequalities, we get:

1. (0, 4):

6(0) - 4(4) = -16 ≤ 18 (satisfies the first inequality)

-2(0) + 7(4) = 28 ≤ 28 (satisfies the second inequality)

2. (3, 0):

6(3) - 4(0) = 18 ≤ 18 (satisfies the first inequality)

-2(3) + 7(0) = -6 ≤ 28 (satisfies the second inequality)

3. (6, 4):

6(6) - 4(4) = 20

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Here are the answers part-wise.

Part A
Considering the current state of the economy and what you know about monetary policy, the Federal Reserve should keep interest rates constant. The reason is that the current environment is conducive to a low-interest rate environment, which encourages business and consumer investments and helps promote economic growth.

Part B
https://www.marketwatch.com/story/why-the-fed-should-not-raise-rates-now-2020-10-02

Part C
The three main points from the source are:
1. The economy is still recovering from the pandemic and raising interest rates could be detrimental to the recovery;
2. Low-interest rates help encourage borrowing for business investment, which helps promote economic growth;
3. Low-interest rates allow businesses and consumers to manage their debt payments more easily.

Part D
The bias that the author brings to their opinion is that low-interest rates are beneficial for the economy and should not be increased.

Part E
https://www.cnbc.com/2020/09/30/fed-should-hike-rates-because-economic-data-now-justifies-it-top-bank-ceo-says.html

Part F
The three main points from the source are:
1. The economy is performing well and raising interest rates would help maintain this momentum;
2. Low-interest rates have encouraged borrowing, which has created a potential for future inflation;
3. Low-interest rates have increased stock market volatility and therefore raising them could help to reduce it.

Part G
The bias that the author brings to their opinion is that high-interest rates are beneficial for the economy and should be increased.

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The exponential function that best matches the graph is given as follows:

E. y = 4^(x + 1).

An exponential function, with horizontal asymptote at y = 0, is defined as follows:

y = ab^x.

In which:

From the graph, when x = 0, y = 4, hence the parameter a is given as follows:

a = 4.

When x = -1, y = 1, meaning that when x increases by one, y is multiplied by 4, hence the parameter b is given as follows:

b = 4.

Hence the function is defined as follows:

y = 4(4)^x

y = 4^(x + 1).

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Answer:

(2, 6), (4, 8), (6, 10), (8, 12), (10, 14)

Answer:

the total number of students on the honor roll increased by 13.8%.

Step-by-step explanation:

Last year, there were a total of 50 + 80 = 130 students on the honor roll.

This year, the number of boys on the honor roll increased by 20%, which means there are now 1.2 * 50 = 60 boys on the honor roll.

The number of girls on the honor roll increased by 10%, which means there are now 1.1 * 80 = 88 girls on the honor roll.

The total number of students on the honor roll this year is 60 + 88 = 148.

The percentage increase in the total number of students on the honor roll is (148-130)/130 * 100% = 13.8%.

Rounding to the nearest tenth, we get that the total number of students on the honor roll increased by 13.8%.

The numbers are written in their standard and scientific notations as follows. Fill in the missing values accordingly.

3.0 * 10⁴ = 3000

6.79 * 10⁻³ =  0.00679

0.0216 = 2.16 * 10⁻²

9.02 * 10⁷ = 90200000

1000000 = 10⁶

1.02 * 10⁻⁵ = 0.0000102

0.000723 = 7.23 * 10⁻⁴

9.99 * 10⁹ = 990000000

56000 = 5.6 * 10⁴

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It is also called standard form or standard index form e.g  1000000 = 10⁶ and 0.0001 = 10⁻⁴

3.0 * 10⁴ = 3.0 * 10000 = 3000

6.79 * 10⁻³ = 6.79 * 0.001 = 0.00679

0.0216 = 2.16 * 10⁻²

9.02 * 10⁷ = 9.02 * 10000000 =  90200000

1000000 = 10⁶

1.02 * 10⁻⁵ =  1.02 * 0.0001 = 0.0000102

0.000723 = 7.23 * 10⁻⁴

9.99 * 10⁹ = 990000000

56000 = 5.6 * 10⁴

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Therefore , the solution of the given problem of equation comes out to be (1, -4) is a solution to the equation 4x - 2y = 12.

The equivalent sign (=) is used in arithmetic equations to signify the equality of two propositions. It is shown that it is possible to compare various numerical factors by using mathematical techniques, which have served as manifestations of reality. For instance, the equal sign divides the number 12 even the solution y + 6 = 12 in two distinct portions. How many characters also are present from either end of such a character can be calculated. Conflicting symbol readings are prevalent.

Here,

To find the values of missing entries, we can pick any arbitrary value of x and solve for y. Let's take x=1.

4(1) - 2y = 12

Simplifying the equation, we get:

-2y = 8

Dividing both sides by -2, we get:

y = -4

So, when x=1, y=-4. Therefore, the missing entries in the table are (1, -4).

Using this value, we can also check that the equation 4x - 2y = 12 is satisfied:

4(1) - 2(-4) = 4 + 8 = 12

So, (1, -4) is a solution to the equation 4x - 2y = 12.

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The solution to the inequality is x ≤ 1.

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

To solve this inequality, we must first perform the operations on the left side of the equation to get an expression equal to 4. We can start by simplifying the fraction on the left side of the equation. We can multiply both the numerator and denominator by x, which will give us 5x - 3 = x + 2x. We can then add 3 to both sides to get 5x = 3 + 2x, which can then be simplified to 3x = 3. Finally, we can divide both sides by 3 to get x = 1. Therefore, the solution to the inequality is x ≤ 1.

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Answer:

A ∩ B = {6, 12}

Step-by-step explanation:

A ∩ B means only the terms A and B have in common.

Therefore, A ∩ B = {6, 12}