In a test, +3 marks are given for every correct answer and -1 mark are given for every incorrect answer. Sona attempted all the questions and scored +20 marks, though she got 10 correct answers. How many incorrect answers has she attempted? (ii) How many questions were given in the test?

"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."

The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.

The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.

Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.

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The original recipe requires 6 cups of flour and 4 cups of water. If the water is reduced to 2 cups, then 3 cups of flour should be used, found by setting up a proportion.

The recipe calls for 6 cups of flour and 4 cups of water.

To decrease the amount of water used to 2 cups, we can set up a proportion

(flour)/(water) = (6)/(4) = (x)/(2)

where x is the amount of flour needed when 2 cups of water are used.

Simplifying this proportion, we get

4x = 12

Dividing both sides by 4, we get

x = 3

Therefore, when the recipe uses 2 cups of water, 3 cups of flour should be used.

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The value of x will make △ONM similar to △SRQ by the SAS similarity theorem is (2/5).

Let us consider the triangles △ONM and △SRQ. To prove their similarity, we need to show that they have two pairs of corresponding angles that are congruent and a proportional side length.

We can see that angle O is congruent to angle S because they are vertical angles. Angle N is congruent to angle R because they are alternate interior angles formed by parallel lines.

To find the proportional side length, we can use the fact that the corresponding sides of similar triangles are proportional. In this case, we can compare the sides ON and SR since they are corresponding sides. We can set up a proportion:

ON / SR = OM / RQ

Since we know that OM = 8 and RQ = 20, we can substitute those values into the proportion and simplify:

ON / SR = 8 / 20

ON / SR = 2 / 5

Now, we can solve for ON by multiplying both sides of the equation by SR:

ON = (2 / 5) x SR

Therefore, we can say that if we set x equal to 2/5 of the length of SR, then the triangles △ONM and △SRQ will be similar by the SAS similarity theorem.

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Complete Question:

What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?

Answer:

26 is a:

B. Whole number

D. Natural number

E. Integer

F. Rational number

Answer:

B, C, D, E, F or all options except A

Step-by-step explanation:

26 is not an irrational number since irrational numbers cant be put in fraction form while 26 can be. ex: 26/1, 52/2 and so on

26 is a whole number.

whole numbers are 0 1 2 3 4 and so on

26 is a real number

imaginary number example: sqrt of -2

natural numbers are numbers going from 1 to infinity

integers are any number that is not a decimal.

26 is rational since it's not irrational.

Answer:

18 x 6 = 108 so 108

Step-by-step explanation:

Answer:

C. (0.3452, ∞)

Step-by-step explanation:

The interval of t when the population of algae will be greater than 500 is (3.452, ∞)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

The amount of algae in a bloom, P, can be modeled by the equation \(P = t^4 + 6t^3+ 7t^2 + 8t\) where t is measured in weeks.

We need to find the find the interval of t will the population of algae be greater than 500

So, we get an inequality,

\(\Rightarrow P > 500\\\\\Rightarrow t^4 + 6t^3+ 7t^2 + 8t > 500\\\\\Rightarrow t (t^3 + 6 t^2 + 7 t + 8) > 500\\\\\Rightarrow t [t [t (t + 6) + 7] + 8] > 500\\\\\Rightarrow t > 3.45~~and ~~t < -6.759\\\\\)

But time is measured in weeks.

So, t will not have the values from the interval (−∞, −6.759)

Therefore, the interval of t when the population of algae will be greater than 500 is (3.452, ∞)

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Answer:

5/18 is a rational number because a rational number is any integer,fraction terminating decimal,or repeating decimal.

5/18 is rational number.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter Q stands for the set of rational numbers. Look at the following illustration to see what a rational number looks like.

Given:

5/18

For rational we need to first divide the fraction and then check whether the fraction is a decimal or not.

Or if it is a decimal then it is terminating or non terminating

5/18 = 0.2777777777777778

Hence, it is terminating  because rational number is any integer, fraction terminating decimal or repeating decimal.

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Based on the graph, a solution for the system of equations is 6 and 3.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of small boxes purchased and number of large boxes purchased, and then translate the word problem into algebraic equation as follows:

Since each small box contains 200 nails and each large box has 600 nails, with a total of 3000 nails;

200x + 600y = 3000.      ..........equation 1.

Additionally, the contractor bought twice as many small boxes as large boxes;

x = 2y                      ..........equation 2.

Next, we would use an online graphing calculator to graphically solve the system of linear equations. Therefore, the required solution for the given system of linear equations is the point of intersection of the two (2) lines on the graph, which is given by the ordered pair (6, 3)

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Answer:

y = -338

Step-by-step explanation:

The equation will be,

→ -26 = y ÷ 13

→ y/13 = -26

Now the value of y will be,

→ y/13 = -26

→ y = -26 × 13

→ [ y = -338 ]

Hence, the value is -338.

Answer:

x = \(\frac{y-5t}{5}\)

Step-by-step explanation:

y = 5(t + x) ← distribute parenthesis by 5

y = 5t + 5x ( subtract 5t from both sides )

y - 5t = 5x ( divide both sides by 5 )

\(\frac{y-5t}{5}\) = x

Answer:The solution is in the attached file

Step-by-step explanation:

The thickness of the film of oil is approximately 1.0315 cubic miles.

Given the total oil spilled is 250 gallons and the area covered by oil is 1.20 square miles, we need to find the thickness of oil film. We can use the formula for this, which is Thickness of oil film = Volume of oil spilled / Area covered by oil.

To find the volume of oil spilled, we first need to convert gallons to cubic miles, which is 1 gallon = 0.00495113 cubic miles. So, 250 gallons of oil is equal to 0.00495113 x 250 = 1.2377825 cubic miles. Now, we can substitute the values in the formula to find the thickness of the oil film.

Therefore, the thickness of the film of oil is approximately 1.0315 cubic miles.

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The solution to the equation (1 - tan² x)/(1 + tan² x) = cos x is all values of x in the domain 0 < x ≤ π.

Given equation: (1 - tan²x)/(1 + tan²x) = cos x

Using the Pythagorean Identity: 1 + tan²x= sec²x

Substituting sec²x into the equation:

(1 - tan²x)/(sec²x) = cos x

Simplifying the equation:

sec²x - tan²x = cos x

Substituting sin² x with 1 - cos² x (from the Pythagorean Identity: sin² x + cos² x = 1):

cos² x + 4 = 4 + cos² x

The equation simplifies to 4 = 4, which is always true.

Therefore, the solution to the equation (1 - tan² x)/(1 + tan² x) = cos x on the domain 0 < x ≤ 2πis all values of x in the domain 0 < x ≤ 2π.

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Answer:

$1.80

Step-by-step explanation:

9x0.2=1.80

He should leave 1.80 as a tip.

Answer:

If you have 3 bags of fertilizer that cover 150 square feet and 2 bags of fertilizer that cover 175 square feet, the total number of square feet that can be covered is:

3 bags x 150 square feet/bag = 450 square feet

2 bags x 175 square feet/bag = 350 square feet

450 square feet + 350 square feet = 800 square feet

So with these total bags of fertilizer, it can cover 800 square feet.

Step-by-step explanation:

Answer:45 x 12 = 450

15 x 10 = 150

35 x 15 = 525

43 x 14 = 602

Step-by-step explanation:

You will need to create this function in your schema using the DDL provided above. Once I review your submission, I will add the function to the HR schema so that it can be utilized for various HR purposes.

The problem identified in the HR schema is the lack of an efficient method to calculate the total years of service for each employee. This information can be useful for HR when making decisions regarding promotions, bonuses, or career development plans. To address this issue, I recommend creating a function that will calculate the total years of service for each employee.
1. Recommended improvement: Create a function called "calculate_years_of_service" to determine the total years of service for each employee in the HR schema.
2. DDL for the function:
```
CREATE OR REPLACE FUNCTION calculate_years_of_service(p_employee_id NUMBER)
RETURN NUMBER
IS
 v_years_of_service NUMBER;
 v_hire_date DATE;
BEGIN
 SELECT hire_date
 INTO v_hire_date
 FROM employees
 WHERE employee_id = p_employee_id;
 v_year_of_service := TRUNC(MONTHS_BETWEEN(SYSDATE, v_hire_date)/12);
 RETURN v_years_of_service;
EXCEPTION
 WHEN NO_DATA_FOUND THEN
   RAISE_APPLICATION_ERROR(-20001, 'Employee not found');
END calculate_years_of_service;
3. You will need to create this function in your schema using the DDL provided above. Once I review your submission, I will add the function to the HR schema so that it can be utilized for various HR purposes.

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y =\((x/2)^2 + 1 or y = (x/2)^2 + 1\)

The curve represents a parabola opening upwards. It is symmetric about the y-axis.

Let's eliminate the parameter t and sketch the curves for each exercise:

1. x = t^2 + 2t, y = t + 1

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 + 2t = x

t = -1 ± √(x + 1)

Substituting the expression for t into the equation y = t + 1, we get:

y = (-1 ± √(x + 1)) + 1

y = -√(x + 1) or y = √(x + 1)

The curve represents two branches of a parabola opening upwards. It is symmetric about the y-axis.

2. x = cos(t), y = sin(t), (0, 2π]

Eliminating the parameter t, we obtain:

\(x^2 + y^2 = cos^2(t) + sin^2(t) \\= 1\)

The curve represents a circle centered at the origin with a radius of 1. It covers a full revolution (360 degrees or 2π) in the counterclockwise direction.

3. x = 2t + 4, y = t - 1

By eliminating the parameter t, we have:

t = (x - 4) / 2

Substituting this expression into the equation for y, we get:

y = ((x - 4) / 2) - 1

y = (x - 6) / 2

The curve represents a line with a slope of 1/2 and a y-intercept of -3. It is inclined upwards from left to right.

4. x = 3 - t, y = 2t - 3, 1.5 ≤ t ≤ 3

Eliminating the parameter t, we have:

t = 3 - x

Substituting this expression into the equation for y, we get:

y = 2(3 - x) - 3

y = 6 - 2x - 3

y = -2x + 3

The curve represents a line with a slope of -2 and a y-intercept of 3. It is inclined downwards from left to right.

\(5. x = 2t^2, y = t^4 + 1\)

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 = x/2

t = ±√(x/2)

Substituting the expressions for t into the equation y = t^4 + 1, we get:

y = (√(\(x/2))^4\) + 1 or y = (-√\((x/2))^4\) + 1

\(y = (x/2)^2 + 1 or y = (x/2)^2 + 1\)

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Answer:

Step-by-step explanation:

C and x

Please mark me brainliest

Wherever you see the letter \(x\) in the equation, you write \(4\), \(0\) or \(-4\) and perform arithmetic operations. Good luck!

EXPLANATION:

We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.

Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.

We can now extract the following triangle from the diagram provided;

We now have a right triangle which we shall solve by use of the Pythagorean theorem;

Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;

Subtract 36 from both sides;

Take the square root of both sides;

Rounded to the nearest tenth, the answer is;

ANSWER:

Answer: The volume of the cone is 130 cubic centimeters.

Step-by-step explanation:

We know that to find the volume of a cylinder you will use the formula

V= \(\pi\)\(r^{2} *h\)  Where r is the radius and h is the height.

And to find the volume of a cone you will use the formula

V= \(\pi\)\(r^{2}\)*h /3

So if they have the same dimensions which is the height and the radius then we will just divide the  volume of the cylinder by 3 to find the volume of the cone.

V = 390/3

V =  130 cm^3

To find the angle of the adjacent side in a triangle with an opposite side of 9cm and an angle of 23 degrees, we can use the sine function. The angle of the adjacent side in the given triangle is approximately 66.42 degrees. The angle of the adjacent side is approximately 39.42 degrees.

In a right triangle, the side opposite to an angle is called the opposite side, and the side adjacent to the angle is called the adjacent side. To find the angle of the adjacent side, we can use the sine function, which relates the ratio of the opposite side to the hypotenuse of a right triangle. The sine of an angle is calculated by dividing the length of the opposite side by the length of the hypotenuse.

In this case, we are given the length of the opposite side (9cm) and the angle (23 degrees). Let's assume the hypotenuse is h. Using the sine function, we can write:

sin(23 degrees) = 9cm / h

To find the value of h, we can rearrange the equation:

h = 9cm / sin(23 degrees)

By calculating the value of sin(23 degrees) using a scientific calculator or trigonometric table, we get approximately 0.3907. Substituting this value back into the equation, we find:

h = 9cm / 0.3907 ≈ 23.03cm

Now, we can use the cosine function to find the angle of the adjacent side:

cos(adjacent angle) = 9cm / 23.03cm

Simplifying this expression, we get:

cos(adjacent angle) ≈ 0.3907

To find the adjacent angle, we can take the inverse cosine (or arccos) of 0.3907 using a calculator, which gives us approximately 66.58 degrees. However, since the given angle is 23 degrees, we subtract this value from 90 degrees to find the angle of the adjacent side:

adjacent angle = 90 degrees - 23 degrees ≈ 66.42 degrees

Therefore, the angle of the adjacent side in the given triangle is approximately 66.42 degrees.

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The equation for the ellipse is x²/625 + y²/400 = 1

To write an equation for an ellipse centered at the origin, which has foci at (0,±15) and vertices at (0,±25),

we use the formula:

x²/a²+y²/b²=1

where a represents the distance from the center to the vertex and c is the distance from the center to the focus.

The distance from the center to the foci is 15 and the distance from the center to the vertices is 25.

The center is located at the origin which means (h, k) = (0, 0).

Thus, a=25, c=15

Since c is the distance from the center to the focus, then

b² = a² − c²

where a = 25 and c = 15.

Substituting in the formula:

b2 = 25² − 15²

b2 = 400

Thus, the equation for the ellipse is:

x²/625 + y²/400 = 1

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Answer:

Step-by-step explanation:

To find the distance between two points, you can use the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

where (x1, y1) and (x2, y2) are the coordinates of the two points.

To find the midpoint between two points, you can use the midpoint formula:

[(x1 + x2)/2, (y1 + y2)/2]

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the given lengths, you should be able to find the coordinates of each point and then use the formulas above to fill out the table in the "Rooftop Artist" document.

Answer:

Step-by-step explanation:

2x + 1 = 4x - 19

Solve for x

2x + 1 = 4x - 19

2x - 4x = -19 - 1

-2x = -20

x = 20 : 2

x = 10

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

check

2 * 10 + 1 = 4 * 10 - 19

21 = 21

the answer is good

Answer: \(\Large\boxed{x=10}\)

Step-by-step explanation:

2x + 1 = 4x - 19

Add 19 on both sides

2x + 1 +19 = 4x - 19 + 19

2x + 20 = 4x

Subtract 2x on both sides

2x + 20 - 2x = 4x - 2x

20 = 2x

Divide 2 on both sides

20 / 2 = 2x / 2

\(\Large\boxed{x=10}\)

Hope this helps!! :)

Please let me know if you have any questions

An equation of the line that passes through the given point and is

(a) parallel to is y = -3x - 7

(b) perpendicular to is y = (1/3)x + 1/3.

a) Parallel line

The slope of the given line is -3. The slope of a parallel line is also -3. So, the equation of the parallel line will be of the form:

y = -3x + b

Plug the point (-2, -1) into this equation to solve for b, the y-intercept.

-1 = -3(-2) + b

-1 = 6 + b

-7 = b

Therefore, the equation of the parallel line is:

y = -3x - 7

b) Perpendicular line

The slope of a perpendicular line is the negative reciprocal of the slope of the given line. The slope of the given line is -3, so the slope of the perpendicular line is 1/3. So, the equation of the perpendicular line will be of the form:

y = (1/3)x + b

Plug the point (-2, -1) into this equation to solve for b, the y-intercept.

-1 = (1/3)(-2) + b

-1 = -2/3 + b

1/3 = b

Therefore, the equation of the perpendicular line is:

y = (1/3)x + 1/3

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Answer:

hm? is there any picture that they gave you or no?

Step-by-step explanation: