Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = − 8 x=-8 and x = − 4 x=-4 and passes through the point ( 0 , − 7 ) (0,-7) .
The formula for a parabola with roots at x=-8 and x=-4, and which passes through the point (0,-7), is y = -7/32(x + 4)(x + 8).
Explanation:The formula we're looking for is in the form of a quadratic function, generally expressed as
y = ax² + bx + c. Our roots are -8 and -4, which we represent in the factors of the equation as (x + 4) and (x + 8). As coefficients multiply to a, we seek a that makes our function pass through the specific point (0, -7). Thus, we substitute the point into the function giving -7 = a(0+4)(0+8) leading us to a = -7/32. So, the equation of the parabola asked is
y = -7/32(x + 4)(x + 8).
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What is the center of the circle represented by this equation? x^2 + (y + 9)^2 = 25 A) (3, 5) B) (0, 25) C) (9, 25) D) (0, -9)
What is the amplitude of the function below?
Whats the sum 3/x + 4/x^2
Answer:
[tex]\frac{3x+4}{x^2} [/tex]
Step-by-step explanation:
sum of [tex]\frac{3}{x} + \frac{4}{x^2}[/tex]
To find the sum of two fractions we need to make the denominator same
LCD is x^2. we need to get x^2 in the denominator of both fractions
Multiply the first fraction with x
[tex]\frac{3 \cdot x}{ \cdot x} + \frac{4}{x^2}[/tex]
[tex]\frac{3x}{x^2} + \frac{4}{x^2}[/tex]
Denominators are same , now we add the numerators
[tex]\frac{3x+4}{x^2} [/tex]
If $8,500 is deposited in a compound interest account paying 3.9% interest annually, how much will be in the account after 12 years? Round your answer to the nearest cent.
The formula for amount is given by:
[tex] A=P(1+\frac{r}{n})^{nt} [/tex]
Now we are given ,
Principal (P) =$8500
rate (r) =3.9% = 0.039
period of interest (n) =1 for compounded annually
time (t) = 12 years
Plugging these values in the formula,
[tex] A=8500(1+\frac{0.039}{1})^{1*12} [/tex]
Amount =$13452.5773053
Answer : There will be $13452.5773053 in the account after 12 years.
What is the value of a, if a2 – 64 = 0 and a > 0?
What is the area of the figure below? Please explain!
|x+18|=1
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Balancing chemical equations lab answers is the number of total molecules on the left side of a balanced equation always equal to the number of total molecules on the right side of the equation?
Yes, in a balanced chemical equation, the number of total molecules (or atoms) on the left side of the equation is always equal to the number of total molecules (or atoms) on the right side of the equation. This principle is known as the Law of Conservation of Mass.
The Law of Conservation of Mass states that in a chemical reaction, matter is neither created nor destroyed. This means that the total mass of the reactants must be equal to the total mass of the products. Since molecules are composed of atoms, the number of atoms of each element on the left side of the equation must equal the number of atoms of the same element on the right side of the equation.
To balance a chemical equation, coefficients are placed in front of the chemical formulas to ensure that the number of atoms of each element is the same on both sides of the equation. Balancing the equation ensures that the total number of molecules (or atoms) is conserved, maintaining the principle of the Law of Conservation of Mass. Therefore, in a balanced chemical equation, the number of total molecules on the left side is always equal to the number of total molecules on the right side.
COMPLETE QUESTION:
Balancing chemical equations lab answers is the number of total molecules on the left side of a balanced equation always equal to the number of total molecules on the right side of the equation?
Please help me with this question:
Riley made a scale drawing of a triangular clock face. Riley used a scale factor of 3 when making her drawing. If the base and the height of Riley's drawing are 10 centimeters and 15 centimeters respectively, what is the area of the triangular clock face?
A. 75 square centimeters
B. 225 square centimeters
C. 675 square centimeters
D. 2,700 square centimeters
An airline sells all tickets for a certain route at the same price. if it charges 250 dollars per ticket it sells 5000 tickets. for every 5 dollars the ticket price is reduced, an extra 500 tickets are sold. it costs the airline a hundred dollars to fly a person. what price will generate the greatest profit for the airline?
Answer:
Scenario II i.e. when the price of ticket is $[tex]$245[/tex] will generate the greatest profit for the airline
Step-by-step explanation:
Scenario I
[tex]5000[/tex] tickets are sold at $ [tex]250[/tex] per ticket
The total money earned by the flight agency is
Number of tickets x price of each tickets
[tex]= 5000 * 250\\[/tex]
[tex]= 1250000[/tex] dollars
Scenario II
The price of each ticket is reduced by $[tex]5[/tex]
The price of new ticket is
[tex]250 -5[/tex]
[tex]= 245[/tex] dollars
The new number of tickets sold after reducing the price is
[tex]5000+ 500\\[/tex]
[tex]5500[/tex]
The total money earned by the flight agency is
Number of tickets x price of each tickets
[tex]5500 * 245\\[/tex]
[tex]1347500[/tex] dollars
Scenario II i.e. when the price of ticket is $[tex]$245[/tex] will generate the greatest profit for the airline
Find two different sets of parametric equations for the given rectangular equation (there are many correct solutions)
x^2+4y^2 - 16=0
A shipment of 20tvs contains 5 that are defective. if 10 of them are randomly chosen for inspection, what is the probability that 2 out of 10 will be defective?
Final answer:
Using the hypergeometric distribution, the probability that exactly 2 out of 10 TVs randomly chosen from a shipment of 20 are defective is approximately 34.81%.
Explanation:
To find the probability that exactly 2 out of 10 randomly chosen TVs are defective, we can use the hypergeometric distribution. This distribution applies because we are dealing with a scenario where we have a finite population (20 TVs) and a non-replacement condition (once a TV is chosen for inspection, it is not put back).
The probability formula for the hypergeometric distribution is:
P(X = k) = [(C(g, k) * C(N-g, n-k)) / C(N, n)]
Where:
C(a, b) is the combination of a items taken b at a time.N is the total number of items in the population (20 TVs).g is the number of defective items in the population (5 defective TVs).n is the number of items chosen (10 TVs inspected).k is the number of defective items we're interested in finding within the chosen items (2 defective TVs).Plugging the numbers into the formula, we have:
P(X = 2) = [(C(5, 2) * C(15, 8)) / C(20, 10)]
P(X = 2) = [(10 * 6435) / 184756]
P(X = 2) = [64350 / 184756] ≈ 0.3481
So, the probability that exactly 2 out of 10 TVs inspected will be defective is approximately 0.3481 or 34.81%.
Find two numbers, if their sum is (−1/3) and their difference is 18
what is the distance between the two points located at 9,12 and 9,-11
A survey found that 25% of pet owners had their pets bathed proffesionally rather than doing it themselves. If 18 pet owners are randomly selected, the probability that exactly 5 people have their pets bathed proffesionally is
A. 19.99%
B. 19.88%
C. 18.99%
D. 18.88%
If f(x) = −2 + 8, what is f(−1.8)?
Cedric has $0.45 in his pocket which fraction of a dollar does Cedric have
Cedric has 9/20 of a dollar.
Explanation:To find the fraction of a dollar that Cedric has, we need to convert $0.45 into a fraction with a denominator of 100, which represents cents. Since 1 dollar is equal to 100 cents, we can write $0.45 as 45 cents. So, Cedric has 45/100 of a dollar, which can be simplified to 9/20.
Find the absolute maximum and minimum of values of the set
d. f(x,y)= 2x^2+y^2-4x-2y+1 d={(x,y) | 0 <= 3, 0 <= y <= 2}
on wednesday, 30 students went to after school tutoring. on thursday, 6 students went. what is the percent decrease in the numbers of students who went to toturing?
Answer:
the number decreased by 80%
Step-by-step explanation:
The percentage change can be computed using ...
percent change = ((new value)/(old value) -1) × 100%
Putting the given numbers into this equation gives ...
percent change = (6/30 -1) × 100% = -4/5 × 100%
percent change = -80%
A negative sign on the percent change means the change was a decrease. The number of students who went to tutoring decreased by 80%.
Answer:
thanks
Step-by-step explanation:
andy earned $38 on monday and $34 on tuesday.how many lucky bamboo plants can he buy with the total money he earned?
A pitcher of fruit punch holes 2 gallons of nine people share the entire pitcher equally how much punch does each person get?
At the Golden Gopher Mall , 1,300 People Took the Coke/Pepsi Challenge, 55% Of those challenged preferred Coke. how many people selected coke?
Wastewater is filling barrels at the rate of 11 quarts per hour. The recycling facility picks up 120 full barrels on each trip, and each barrel holds 12 quarts of wastewater. How many days are between each pickup? Show your work to receive full credit. (10 points)
The sum of a number (n) and 20 is 55. Which equation shows this relationship?
Find the trace on the xy-plane of the sphere having center at (−1, 3, −1) and radius 2.
Final answer:
The trace on the xy-plane of a sphere with center (-1, 3, -1) and radius 2 is a circle with center (-1, 3) and radius 2, represented by the equation (x + 1)² + (y - 3)² = 4.
Explanation:
The question asks to find the trace on the xy-plane of the sphere having a center at (-1, 3, -1) and a radius 2.
The trace on the xy-plane of a sphere is essentially the circle that is formed when the sphere intersects the xy-plane.
Since the center of the sphere is (-1, 3, -1), and the sphere intersects the xy-plane (z=0), we keep the x and y coordinates of the center the same for the circle, meaning the center of the circle will be (-1, 3). The radius of the circle remains the same as the sphere, which is 2.
The equation for a circle in the xy-plane with center (h, k) and radius r is given by (x - h)² + (y - k)² = r².
Therefore, plugging in the values for this specific circle gives us the equation (x + 1)² + (y - 3)² = 4.
This equation represents the trace of the sphere on the xy-plane.
Find the probability of the independent event. 7) if p (e) = 0.9, p (f ∣
e.= 0.36, and e and f are independent, find p (f).
I’m going to cook a turkey for 14 people and I want to allow 3/4ib of turkey for each person 1ib=450g what size will I need
To find the size of turkey needed for 14 people, multiply their serving size by the number of people and convert it from pounds to grams
Explanation:To calculate the size of turkey you will need, you first need to find the total weight of the turkey required for 14 people. Since you want to allow 3/4 lb of turkey for each person, the total weight of turkey required will be 14 * 3/4 lb.
Now, 1 lb is equal to 450g. So, to convert the weight from pounds to grams, you can multiply the weight in pounds by 450.
Therefore, to find the size of turkey you will need, multiply the total weight of turkey required in pounds (14 * 3/4) by 450. This will give you the answer in grams.
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a motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.
please help slove and steps
Answer:
the answer is 12
hope i helped
Step-by-step explanation:
Thirty runners compete in a cross country race. your school has five runners in the race. what is the probability that three runners from your school place first, second, and third.
The probability that three runners from the same school finishing first, second, and third can be calculated as the product (5/30) * (4/29) * (3/28). This uses the principles of probability in mathematics.
Explanation:The problem involves the concept of probability in Mathematics. Let's break this question down using the principles of probability.
For the first runner to be from your school, the probability would be 5/30 as there are 5 runners from your school out of 30 total runners. After one runner from your school has won, there are now 4 runners left from your school and 29 total runners left. So, the probability of the second runner being from your school is 4/29. Similarly, the probability that the third runner is also from your school is 3/28 since there are now three left from your school and 28 in total.
The final probability is the product of all three of these probabilities, so:
P(all three top spots are from your school) = (5/30) * (4/29) * (3/28), which needs to be calculated to get the final result.
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The result is 0.00246, or about 0.25% chance.
To find the probability that three runners from your school place first, second, and third in a race with 30 runners, we need to consider the number of ways to select these three positions from your school's five runners and divide it by the total number of ways to select any three runners from all 30 participants.
Calculate the number of ways to choose 3 runners out of the 5 from your school:
[tex]C(5, 3) = \( \frac{5!}{3!(5-3)!} \) = 10[/tex]
Calculate the number of ways to arrange these 3 runners in the first, second, and third positions. This is equal to the number of permutations of 3 elements:
P(3) = 3! = 6
Calculate the total number of ways to choose 3 runners out of the 30 participants:
[tex]C(30, 3) = \( \frac{30!}{3!(30-3)!} \) = 4060[/tex]
Calculate the number of ways to arrange these 3 runners in the first, second, and third positions:
P(3) = 3! = 6
Finally, calculate the probability that 3 runners from your school place first, second, and third:
[tex]Probability = \( \frac{C(5, 3) \times P(3)}{C(30, 3) \times P(3)} \) = \( \frac{10 \times 6}{4060 \times 6} \) = \( \frac{10}{4060} \) = \( \frac{1}{406} \)[/tex]
Thus, the probability is approximately 0.00246 (or 1/406).