Coordinate system Questions and Answers

What is the directrix of the parabola y = -8x²? Simplify any fractions.

What is the directrix of the parabola y= x² + 6 ?.Simplify any fractions. ________

What is the directrix of the parabola y= -(5x²) - 3? Simplify any fractions.

The equation of a parabola is y = x² +( 4x) + 13. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

Draw an image of the following mapping and name the type of mapping. (x,y) - >(x-6,y+4) (x,y) → (x-6, y+4) Type of mapping: _______

What is the axis of symmetry of the parabola y = -9x² - 5?

What is the focus of the parabola y = 4x²?

The equation of a parabola is y=-x² + (12x) - 29. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

What is the axis of symmetry of the parabola y =( -1/5)(x − 6)² + 4?

What is the focus of the parabola y = -4x² - 1? Simplify any fractions.

Graph. Be sure to label the vertices. a) (24x^2 )+ (2y^2) = 72. b) {36(x-5)^2} + {4(y-2)^2} = 36.

Sketch the graph of the function. Describe how each graph can be obtained from the graph of a basic exponential function. f(x)=(2^x-1)-3

The probability of event A is 0.56, and the probability of event Bis 0.34. If A and B are independent events, then P(A and B) =

Malik randomly picked two numbers from 1 to 9 (including 1 and 9). The same number could be picked more than once. The first of the two numbers he picks is odd and less than 5. What is the probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5?____

Convert the equation in standard form to point-normal form for a plane in R³: a. 2x-y+2=5 b. 2x + 3y = 1 c. z=0

A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is____units. The point (-15,____)lies on this circle.

The equation of a circle is x²+y²+ Cx+ Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point. how are the coefficients C, D, and E affected?

A cake shop bakes a variety of brownies. The top-selling brownies are ones with toppings of chocolate chip, walnuts, or both. A customer enters the store. The probability that the customer will pick both toppings is 0.4. What is the probability that they will pick neither the chocolate chip nor the walnut toppings? A 0.5 B. 0.3 C. 0.45 D. 0.8 E. 0.2

The probability of Samantha scoring an A on a geology test (event A) is 0.46, and the probability of Judith scoring an A on the same test (event B) is 0.54. The probability of both Samantha and Judith scoring an A is 0.2484. Given this information, which statement is true? A Events A and B are independent because P(A and B)=P(A)*P(B). B Events A and B are independent because P(B|A) ≠ P(B). C Events A and B are dependent because P(A and B)=P(A) x P(B). D Events A and B are dependent because P(AIB)≠P(B).

Based on the data in this two-way table, if a flower is picked at random, what is the probability of getting a yellow flower? Type of Flower/Color Red Pink Yellow Total Rose 40 20 45 105 Hibiscus 80 40 90 210 Total 120 60 135 315 A. 0.190 B. 0.333 C. 0.381 D. 0.429

A class consists of 55% boys and 45% girls. It is observed that 25% of the class are boys and scored an A on the test, and 35% of the class are girls and scored an A on the test. If a student is chosen at random and is found to be a girl, the probability that the student scored an A is ______

A quadrilateral has vertices A(4, 5), B(2, 4), C(4, 3), and D(6, 4). Which statement about the quadrilateral is true? A. ABCD is a parallelogram with noncongruent adjacent sides. B. ABCD is a trapezoid with only one pair of parallel sides. C. ABCD is a rectangle with noncongruent adjacent sides. D. ABCD is a square. E. ABCD is a rhombus with non-perpendicular adjacent sides.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the trigonometric ratios with their values based on the triangle shown in the diagram. a)sin D b)sinC c)sin DXcos D d)tanCxtanD

Franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6. The probability that the sum of the numbers rolled is either even or a multiple of 5 is ____ . The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is ____.

The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9 is ____. The probability that both the first digit and the last digit of the three-digit number are even numbers is _____.

In a factory, the chance that a certain machine works without overheating in the morning is 50%. If it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. What is the probability that on a given day it will work in the morning and overheat later on? A. 4% B. 3.75% C. 7.5% D. 3.5%

Kayla has a bowl of beads that contains 42 yellow beads, 28 green beads, 12 white beads, and 18 red beads. She randomly draws a bead from the bowl. The probability of Kayla not drawing a yellow or a green bead is ____ The probability of Kayla drawing a red or a green bead is____%

John is playing a game of darts. The probability that he throws a dart into the center of the dart board (the Bull's eye) is 10. The probability that he throws the dart into the 10-point ring is 3/10. What is the probability that he either hits a Bull's eye or scores 10 points? A. 1/3 B. 2/3 C. 3/5 D. 2/5 E. 1/4

The probability that a comic book reader in a particular city prefers comics published by Company A is 25%. The probability that a comic book reader in the city is male is 70%. If the probability of a comic book reader in the city being a male, given that the reader prefers Company A's comics, is 40%, what is the probability of the reader preferring Company A's comics, given that the reader is a male? A. 0.14 B. 0.25 C. 0.30 D. 0.45

A number is selected at random from the set (2. 3. 4. ... 10). Which event, by definition, covers the entire sample space of this experiment? A. The number is greater than 2. B. The number is not divisible by 5. C. The number is even or less than 12. D. The number is neither prime nor composite. E. The square root of the number is less than 3.

Select the correct answer from the drop-down menu. In the figure, m∠B = m∠C and ∠D is a right angle. COS β=

Let I be the line with parametric equations x=-1-3t y = 10-3t z = -5-3t Find the vector equation for a line that passes through the point P=(10, -9, 4) and intersects L at a point that is distance 5 from the point Q= (-1, 10,-5). Note that there are two possible correct answers. Use the square root symbol '' where needed to give an exact value for your answer.

Type the correct answer in the box. Write your answer as a reduced fraction, using / for the fraction bar. A six-sided fair die is rolled 4 times in a row. The probability of getting a 4 only on the last trial is____

A school choir has 80 students; 36 of them are in seventh grade. Also, 40 students in the choir are girls: 18 of them are in seventh grade. What is the probability that a student picked at random from the choir is either a girl or is in seventh grade? A. 27/40 B. 29/40 C. 13/40 D. 33/40

Which equation implies that A and Bare independent events? A) P(B | A) = P(A) B). P(A | B) = p(B | A) C). P(A) = P(B) D). P(A⋂B) = P(A) × P(B) E) P(A⋂B) = P(A) P(B)

The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8). The x-intercepts of the parabola are_____and____

Select the correct answer from each drop-down menu. Two six-sided fair dice are rolled simultaneously. The probability that the sum of the two numbers rolled is greater than 3, given that the sum of the numbers is not greater than 5, is___ The probability that one of the numbers is a 6 and the sum of the two numbers is an odd number is____

Based on the data in the two-way table, what is the probability that a person consumes 1.500 to 2,000 calories in a day? A. 0.22 B. 0.28 C. 0.35 D. 0.50

A television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and receives a report assessing favorable or unfavorable viewer response. In the past, 60% of the network's shows have received a favorable response from viewers, and 40 % have received an unfavorable response. If 50% of the network's shows have received a favorable response and have been successful, and 30% of the network's shows have received an unfavorable response and have been successful, what is the probability that this new show will be successful if it receives a favorable response? A. 0.41 B. 0.53 C. 0.67 D. 0.70 E. 0.83

In ∆MNP, Q divides MP into the ratio of 4:3 and NQ divides MR into the ratio of 2:1 where R is a point on NP. What ratio does MR divide NQ into?

Triangle QRS has been translated to create triangle QRS. RS = RS 2 units, angles S and S are both 28 degrees, and angles R and I are both 32 degrees. Which postulate below would prove the two triangles are congruent? a SSS b SAS c ASA d AAS

A writer sells 100 call options with strike $42 for $0.91 each and deposits these premiums in a bank. The calls mature in 30 days, and the bank's interest rate over those 30 days is 5%. At expiry the underlying asset of the call is worth $39 each. At expiry, the writer withdraws all cash from the bank, purchases the necessary amount of shares on the open market and completes the call contract. What is the writer's profit? Give your answer correct to two decimal places, and if the writer makes a loss include a minus sign.

A convex polyhedron is made out of equilateral triangles and regular octagons. One equilateral triangle and two octagons meet at each vertex. Determine the number of vertices, faces, and edges in the polyhedron.

Find the unit rates. If necessary, round your answers to the nearest hundredth. $6.19 for 8 pounds ______dollars per pound ______pounds per dollar.

A circle with circumference 12 has an arc with a 330° central angle. What is the length of the arc?

If DE = 4x-1, EF = 9, and DF = 9x-22, find the value of x.

The number of branches on a tree demonstrates the Fibonacci sequence. How many branches would there be on the next two levels of this tree? 13 8 2 5 3 2 1 branches A. 34, 55 B. 21,34 C. 18, 28 D. 21, 29

A circle is inscribed in a square with a side length of 94. If a point in the square is chosen at random, what is the probability that the point is inside the circle? Round your answer to the nearest tenth of a percent. ______ %

CONSTRUCTION The frame for the roof of a house is designed so that the ratio of the rise to the run is in a constant ratio of 5/12.What is the measure of angle A to the nearest degree? A) 23° B) 25° C) 65° D) 67°

At her party, Emily wants to serve each of her friends a hotdog and a bun. There are 8 hotdogs in a package but only 6 buns in a bag. What is the least amount of hotdogs Emily must buy so that she has the same amount of hotdogs and buns? A. 48 B. 16 C. 8 D. 24