Answer:
a, c and d
Step-by-step explanation:
j by 9 and then multiply the quotient by 2
The sequence of the questions is [tex]J/9[/tex] when you multiply [tex]J[/tex] by [tex]9[/tex] and the quotient by [tex]2[/tex].
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the result, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.
Is quotient the same as answer?The result of dividing two integers is known as the quotient. Six divided into two results in the number three. Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the two digits enters the first.
[tex]2 * (J/9)[/tex]
This means you first divide [tex]J[/tex] by [tex]9[/tex] to get the quotient, and then multiply the quotient by [tex]2[/tex]. So the order of operations is:
[tex]J/9[/tex]
Multiply the quotient by [tex]2[/tex]
For example, if [tex]J = 45[/tex], then:
[tex]J/9 = 45/9 = 5[/tex]
[tex]2 * (J/9) = 2 * 5 = 10[/tex]
So the result of multiplying [tex]J[/tex] by [tex]9[/tex] and then multiplying the quotient by [tex]2[/tex], when [tex]J = 45[/tex], is [tex]10[/tex].
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(8,-4) and (-1-2) to the nearest tenth
Eva is packing for a camping trip. There are 3 sleeping bags and 2 pillows to choose from. For the tent, Eva has 6 options. In how many different ways can Eva pick a set of camping gear that includes one of each item?
Eva has 36 different combinations of camping gear to choose from.
What are combinations?Combinations are arrangements of a given set of objects, without regard to their order. Combinations are used in mathematics to describe the possible arrangements of a given set of objects.
In this case, there are 3 sleeping bags, 2 pillows, and 6 tents. In order to determine the total number of combinations, Eva would need to multiply 3x2x6 which equals 36.
If she decides to pick a sleeping bag first, then she can pick any of the 3 available sleeping bags. She would then need to pick one of the 2 pillows and one of the 6 tents. If the order in which she selects her gear does not matter, then she can use the same method to determine the number of combinations available.
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The number of ways in which Eva can pick a set of camping gear that includes one of each item is 55.
What is combination?Combination involves selecting items from a set of items without regard to the order in which they are selected. It is typically expressed using the notation C(n,r) which stands for the number of combinations of n items taken r at a time, where n is the total number of items and r is the number of items taken at a time.
This is an example of a combination problem, as Eva is looking to select a set of items from multiple categories, rather than a permutation problem, which would be selecting a set of items where the order matters.
In this case,
n= 6 (the number of tents)+ 3 (the number of sleeping bags)+ 2 (the number of pillows)= 11.
We want to choose 1 of each item, so r is 3.
Plugging 11 and 3 into the formula, we get
11C3 = 11! / (3! * 8!)
= 11 * 10 * 9 / (3 * 2 * 1)
= 11 * 5
= 55
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Question 70 Approximately 38 percent of people living in on Whave the blood type o positive. A random sample of 100 people from region veled people in the samed the Contra Hypothesis test to vestigate whether the percent of people in thegion with positive blood is different from that of tegen wWwth of the following is the property for the H-0.35 He0.35 с Hep -0.35 D Hp 0.35 H: 0.38
Answer: The null hypothesis (H0) is the statement that there is no significant difference between the proportion of people in the region with the O positive blood type (p) and the population proportion (p0) of 0.38.
The null hypothesis is usually denoted as:
H0: p = p0
In this case, p0 is given as 0.38, so the correct answer is:
H0: p = 0.38
Step-by-step explanation:
Suppose P is a predicate over integers, and you would like to prove that for all integers n, P(n) is true. Which of the following are valid proof approaches? Select all correct choices. Select one or more: O a. Show P(1) and that Vk E Z P(k) + P(k + 1) O b. Show P(0), P(1),P(-1) and that Vk E Z P(k) → P(k + 1) c. Show P(0) and that WK EN P(k) → (P(k + 1) ^ P(k – 1)) O d. Show P(0), P(1), P(-1) and that Vk E Z P(k) → P(k – 1) O e. Show P(0), P(1),P(-1) and that Vk e Z+ P(k) → P(k + 1) and Vk e Z+ P(-k) → P(-(k + 1)) O f. Show P(O), P(1) and that Vk e Z+ P(k) → P(-k)
The valid proof approaches are: b. Show P(0), P(1),P(-1) and that Vk E Z P(k) → P(k + 1) and e. Show P(0), P(1),P(-1) and that Vk e Z+ P(k) → P(k + 1) and Vk e Z+ P(-k) → P(-(k + 1))
Approach a is invalid because it only shows that P holds for some integers, but not for all integers.
Approach c is invalid because it only shows that P holds for non-negative integers, but not necessarily for negative integers.
Approach d is invalid because it only shows that P holds for non-negative integers and negative even integers, but not necessarily for negative odd integers.
Approach f is invalid because it only shows that P(0) and P(1) imply P(-k) for all positive integers k, but not necessarily for all integers.
Approach b is a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1) and P(-1), and that if P holds for an arbitrary integer k, then it also holds for k+1.
Approach e is also a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1), P(-1), and that if P holds for a positive integer k, then it also holds for k+1, and if it holds for a negative integer -k, then it also holds for -(k+1).
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A random experiment can result in one of the outcomes {a,b,€,d} with probabilities P({a}) = 0.4, P({b}) = 0.1, P({c}) = 0.3, and P({d}) 0.2. Let A denote the event {a,b}, B the event {b,c,d}, and the event {d} From the previous information , P(A UBUC)= QUESTION 31 A random experiment can result in one of the outcomes {a,b,€,d} with probabilities P({a}) = 0.4, P({b}) = 0.1, P({c}) = 0.3, and P({d}) 0.2. Let A denote the event {a,b}, B the event {b,c,d}, and C the event {d} From the previous information , P(Anenc)=
The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
The given probabilities of events and outcomes are:
P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2
So the given events are:
A = {a,b},B = {b,c,d},C = {d}
We have to find P(A U B U C) Using the formula of the probability of the union of two events,
we get:
P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Now we will find the values of all probabilities:
P(A) = P({a}) + P({b})
= 0.4 + 0.1
= 0.5
P(B) = P({b}) + P({c}) + P({d})
= 0.1 + 0.3 + 0.2
= 0.6
P(C) = P({d})
= 0.2
P(A ∩ B) = P({b})
= 0.1
P(A ∩ C) = P({d})
= 0.2
P(B ∩ C) = P({d})
= 0.2
P(A ∩ B ∩ C) = 0
(No common event) Put all the above values in the formula:
P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +
P(A ∩ B ∩ C)
= 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0
= 0.8
Therefore, P(A U B U C) = 0.8 is the required probability.
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the cylinder has a volume of 45 cubic inches and a height of 5 inches what is the raduis of the cylinder
The radius of the cylinder is 3 inches.
What is the volume of a cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases and a curved lateral surface connecting the two bases. The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex], where r is the radius of the base, h is the height of the cylinder, and π is a constant value approximately equal to 3.14.
Calculating the value of radius :
We are given that the cylinder has a volume of 45 cubic inches and a height of 5 inches. Using the formula for the volume of a cylinder, we get:
[tex]V = \pi r^2h[/tex]
Substituting the given values, we get:
[tex]45 = \pi r^2(5)[/tex]
Simplifying the equation, we get:
[tex]9 = r^2[/tex]
Taking the square root of both sides, we get:
[tex]r = \pm 3[/tex]
Since the radius cannot be negative, we take the positive value of r, which is:
r = 3 inches
Therefore, the radius of the cylinder is 3 inches.
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Como le hago ayuda aaaa
When the area is constant, the proportionality constant, 48, reflects the sum of the base and height.
What does the proportionality constant mean?When two quantities grow and shrink at the same rate, they are directly proportional. The proportionality constant k is defined as k=y/x when y and x are two numbers that are directly proportional to one another.
Using the formula for the area of a rectangle, we can determine the missing data in the table:
Area = base x height
The missing values can be located as follows using the values listed in the table:
Base (b) Height (h) Area
24 2 48
3 8 24
8 3 24
4 6 24
We can apply the inverse variation formula to find the constant of proportionality:
y = k/x
This equation can be changed in order to account for k:
k = xy
Using any pair of values from the table, we can find k as follows:
k = xy = 24(2) = 48
Hence, 48 is the proportionality constant. It is possible to verify that this value applies to all of the value pairs in the table:
For the first pair (b=24, h=2), we have xy = 24 x 2 = 48, which is the constant of proportionality.
For the second pair (b=3, h=8), we have xy = 3 x 8 = 24, which is the area.
For the third pair (b=8, h=3), we have xy = 8 x 3 = 24, which is the area.
For the fourth pair (b=4, h=6), we have xy = 4 x 6 = 24, which is the area.
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Question:
The following table shows some values for the base and height of a rectangle whose area is constant. Write down the missing data.
Base (b)
Height (h)
24
2
3
8
4
4
What is the area of the rectangle?
What kind of variation do you see in this table?
What is the constant of proportionality?
How did you determine the constant of proportionality?
What is the measure of ∠D? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠D= ° A right triangle B C D. Angle C is marked as a right angle. Side B C is labeled as 25 feet. Side C D is labeled as 45 feet.
Therefore, the measure of ∠D is approximately 60.96 degrees.
What is measure?A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.
by the question.
To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:
[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]
Taking the inverse tangent of both sides, we get:
[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]
Rounding this to the nearest hundredth, we get:
[tex]angleD = 60.95 degrees =60.96 degree.[/tex]
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6 : water pours into a fish tank at a rate of 0.3 cubic meters per minute. how fast is the water level rising if the base of the fish tank is a 2 meter by 3 meter rectangle?
Water pours into a fish tank at a rate of 0.3 cubic meters per minute, the water level is rising at a rate of 1/60 m/min
How to calculate the water level?Given
The base of the fish tank is a 2-meter by 3-meter rectangle.The area of the base of the fish tank = length x breadth= 2 m x 3 m = 6 m².Let, h is the height of the water level in the fish tank after t minutes. Then, the volume of the water in the fish tank after t minutes is given by [tex]V = Area of the base * height V = 6 * h m^3[/tex]The rate at which water pours into the fish tank is 0.3 cubic meters per minute.
Therefore, the rate of change of volume of the water in the fish tank after t minutes is [tex]dV/dt = 0.3 m^3/min[/tex]. As per the chain rule of differentiation,[tex]dV/dt = dV/dh *dh/dt[/tex] We have[tex]V = 6h^3m^3 \Rightarrow dV/dh = 18h^2\Rightarrow dV/dt = 18h^2 * dh/dt[/tex] Given that,[tex]dV/dt = 0.3 m^3/min[/tex]. Therefore,[tex]0.3 = 18h^2 * dh/dt \Rightarrow dh/dt = 0.3/18= 1/60 m/min[/tex] Hence, the water level is rising at a rate of 1/60 m/min.
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what is the probability of choosing a red card or a king from a deck of 52 cards? for this event, choosing a red card or choosing a king, where choosing a red card and choosing a king may occur jointly, which rule applies?
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection
How do we calculate the probability?The probability of choosing a red card or a king from a deck of 52 cards is 8/52 or 2/13. To calculate this, we first need to determine the number of cards that are either red or a king. There are 26 red cards in a deck of 52 cards, so the probability of choosing a red card is 26/52 or 1/2. There are four kings in a deck of 52 cards, so the probability of choosing a king is 4/52 or 1/13.
However, we need to be careful to avoid counting the red kings (two of which exist in a deck of 52 cards) twice. To account for this, we subtract the probability of choosing a red king from the sum of the probabilities of choosing a red card and a king. The probability of choosing a red king is 2/52 or 1/26, so the probability of choosing a red card or a king is:
P(red card or king) = P(red card) + P(king) - P(red king)
P(red card or king) = 26/52 + 4/52 - 2/52
P(red card or king) = 28/52
P(red card or king) = 2/13
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection (i.e., the probability that they occur jointly).
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-. If f(x) = x² + 3x-2, find f(x) when x = -2
Answer:
-4
Step-by-step explanation:
substitute -2 into the formula and solve
[tex]f(x)=(-2)^2+3(-2)-2\\f(x)=4+(-6)-2\\\boxed{f(x)=-4}[/tex]
25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:
Total = 25 + (68 - 25) = 43
The ratio of the number of students who have vanilla to the total number of students is:
Vanilla : Total = 25 : 43
This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:
25 : 43
Step-by-step explanation:
Reggie is rolling a block with the number 1,2,3,4, and 5 on it. Kaitlyn is drawing one desk from a basket of three disks: one blue, one red, and one yellow. use the tree diagram below to answer the question. What is the probability that they end up with a yellow disk
Answer:
1/3
Step-by-step explanation:
There is an equal chance of getting a blue, red or yellow disk.
3901 of the original wordle's 10657 allowed guess words have at least one letter repeat, or 36.6%. we can also see that 749 of its 2315 solution words have at least one letter repeat, or 32.3%. how many of the possible 5-tuples of 26 letters (q3.1) have at least one letter repeat? remember: gradescope can evaluate expressions with , -, *, /, ^, ( ), but not factorial.
The original wordle has 10657 allowed guess words. Of which 3901 words have at least one letter repeat. In other words, the probability of the word having at least one letter repeat is 36.6% 749 solution words have at least one letter repeat out of a total of 2315 solution words. the number of possible 5-tuples of 26 letters that have at least one letter repeat is "3987776."
In other words, the probability of a solution word having at least one letter repeat is 32.3%To find the number of possible 5-tuples of 26 letters with at least one letter repeat
Step 1: We will find out the number of 5-tuples that do not have any repeated lettersFor the first letter, we have 26 options. As there can be no repetitions, we have 25 options for the second letter. Similarly, for the third, fourth, and fifth letter we have 24, 23, and 22 options respectively.Therefore, the number of 5-tuples that do not have any repeated letters is given by26 × 25 × 24 × 23 × 22 = 7893600
Step 2: We will find out the number of 5-tuples that have at least one repeated letterTotal number of 5-tuples = 26^5Using the formula for finding the number of 5-tuples without any repetition, we can find the number of 5-tuples that have no repetition:26 × 25 × 24 × 23 × 22 = 7893600 Therefore, the number of 5-tuples that have at least one repeated letter is given by the total number of 5-tuples – the number of 5-tuples that have no repetitions= 26^5 - 7893600= 11881376 - 7893600= 3987776Therefore, the number of possible 5-tuples of 26 letters that have at least one letter repeat is 3987776.
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ratings services measure television audiences. the measurement of the percentage of all households with televisions that are tuned into the same show at the same time is called
Therefore , the solution of the given problem of percentage comes out to be were tuned in to a specific program or show at a given moment.
What is percentage?A number or figure stated as a fraction of 100 is referred to as "a%" in statistics. The versions that begin with "pct," "pct," and "pc" are also uncommon. The common way to indicate it is with the numeral "%," though. Furthermore, there are no indicators and a flat ratio of every single thing to the total number. Percentages are basically integers because they frequently add up to 100.
Here,
The TV ratings, also known as the TV audience share, are a measurement of the proportion of all television-owning households that are watching the same program at the same moment.
Networks and marketers use it as a gauge of a TV show's popularity to decide how successful a program will be and how much to charge for advertising during it.
Companies like Nielsen, which use a sample of homes with televisions to estimate the audience size for a given program or show, are usually in charge of gathering the TV ratings.
TV ratings are expressed as a proportion of all households with televisions that were tuned in to a specific program or show at a given moment.
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Will give brainiest
Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
sunitha is 24 years older than her daughter kavita. 6 years ago, sunitha was thrice as old as kavitha. find their present ages.
67777+776567.55555=?
Answer: 844344.55555
DO THE MATH: Gracie is a manager at Prescribe Pharmaceutical. An employee turned in the timesheet below. Given that Prescribe Pharmaceutical uses the 7-Minute Rule daily for calculating employee hours worked, how many hours did this employee work for the week?
A. 25 hours and 0 minutes
B. 26 hours and 0 minutes
C. 25 hours and 48 minutes
D. 25 hours and 45 minutes
It took 25 hours and 48 minutes employee worked for the week. Thus, option B is correct.
What is a timesheet?A timesheet is a data table which an emplοyer can use tο track the time a particular emplοyee has wοrked during a certain periοd. Businesses use timesheets tο recοrd time spent οn tasks, prοjects, οr clients. There are different methοds that have been used tο recοrd timesheets, such as paper, spreadsheet sοftware, and οnline time-tracking sοftware. Paper-based timesheets have nοw given way tο the digital fοrmats.
1st Day = 12 + 4 pm - 8:45 am
= 16 - 8:45
= 7:15 hours
2nd day = 12 + 5 pm - 9:14 am
= 17 - 9:14
= 7:46 hours
3rd day = 12 + 4:02 pm - 8:30 am
= 16:02 - 8:30
= 7:32 hours
4th day = 12 + 5:00 pm - 9:08am
= 17:00 - 8:30
= 8:30 hours
5th day = 12 + 3:30 pm - 8:07 am
= 15:30 - 8:07
= 7:23 hours
Adding all the hours of work = 7:15 hours + 7:46 hours +7:32 hours + 8:30 hours + 7:23 hours = 25 hours and 48 minutes
Thus, It took 25 hours and 48 minutes employee worked for the week. Thus, option B is correct.
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A building supply has two locations in town. The office receives orders from two of its best customers, each requiring 3/4-inch drywall board to be delivered. Customer A needs at least one hundred sheets delivered and Customer B needs at least one hundred-forty sheets delivered.
Deliveries can be sent from either of the supply companies' warehouses. The warehouse on the north side of town has one hundred-sixty sheets in stock; the south-side warehouse has ninety sheets in stock. Delivery costs per sheet are as follows: $1.50/board from the northern warehouse to Customer A,$1.20/board from the northern warehouse to Customer B, $0.80/board from the southern warehouse to Customer A, and $1.10/board from the southern warehouse to Customer
В.
1. Find the shipping arrangement which minimizes costs.
2. What will be the minimum cost?
3. Will there be any product left in either warehouse after fulfilling the orders?
The shipping arrangement which minimizes costs will be 1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z) subject to
x + z + s1 = 160
y + (240 - x - z) + s2 = 90
x - 100 + s3 = 0
y - 140 + s4 = 0
The minimum cost is $372.00.
There will be product left in either warehouse after fulfilling the orders.
How to explain the informationLet x be the number of sheets delivered from the north-side warehouse to Customer A,
Let y be the number of sheets delivered from the north-side warehouse to Customer B and z be the number of sheets delivered from the south-side warehouse to Customer A.
Then the objective function to be minimized is:
1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z).
There will be 60 sheets of drywall board left in the north-side warehouse and 70 sheets left in the south-side warehouse after fulfilling the orders.
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The Nut House sells pecans worth $4 per pound and cashews worth $8 per pound. How many pounds of pecans and how many pounds of cashews must be
mixed to form 16 lb of a nut mixture worth $6.50 per pound?
Therefore, we need 6 pounds of pecans and 10 pounds of cashews to form 16 pounds of a nut mixture worth $6.50 per pound.
by the question.
Let x be the number of pounds of pecans and y be the number of pounds of cashews in the mixture.
We know that the total weight of the mixture is 16 pounds. Therefore, we have:
[tex]x + y = 16[/tex]
We also know that the mixture is worth $6.50 per pound. This means that the total cost of the mixture is:
[tex]16($6.50) = $104[/tex]
The cost of the pecans is $4 per pound, and the cost of the cashews is $8 per pound. Therefore, the total cost of the pecans in the mixture is 4x, and the total cost of the cashews is 8y. So we have:
4x + 8y = $104
Now we have two equations with two variables. We can solve for x and y using substitution or elimination.
Let's use substitution. We can rearrange the first equation to solve for x:
[tex]x = 16 - y[/tex]
Substitute this expression for x into the second equation:
[tex]4x + 8y = $104[/tex]
[tex]4(16 - y) + 8y = $104[/tex]
[tex]64 - 4y + 8y = $104[/tex]
[tex]4y = $40[/tex]
[tex]y = 10[/tex]
Now we know that there are 10 pounds of cashews in the mixture. We can use the first equation to find the number of pounds of pecans:
[tex]x + y = 16[/tex]
[tex]x + 10 = 16[/tex]
[tex]x = 6[/tex]
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factorise (x-3)²-(x-3)²
Step-by-step explanation:
(x-3)²-(x-3)²
=(x2-6x+9) - (x2-6x+9)
=x2-6x+9-x2+6x-9
=0
In 2010, the population of Belvedere was estimated to be 39,366 people with an annual rate of increase of approximately 2.8%.
Select the explicit expression that represents the population in the next 6 years.
OA. 39,366(1.0028)5
OB. 39,366(1.28)5
OC. 39,366(0.028)
OD. 39,366(1.028)
Based on exponential growth function, the explicit expression that represents the population of Belvedere, which was estimated to be 39,366 in 2020 with an annual increase of 2.8%, in the next 6 years is D. 39,366(1.028)^6.
What is an exponential growth function?An exponential growth function is one of the two exponential function, including exponential decay function.
The exponential growth function is given as y = a(1 + r)^t, where:
y is the new valuea is the current valuer is the constant ratioand t is the time in years.Population of Belvedere in 2010 = 39,366
Annual rate of increase = 2.8%
The time, t = 6 years
Exponential function expression: 39,366(1.028)^6
Thus, the population of the city in the next 6 years can be represented by the expression in Option D.
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What are the roots of the equation 4x^2+16x+25=0 in simplest a+bi form
Answer:
The roots are
[tex]x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i[/tex]
Step-by-step explanation:
4x² + 16x + 25 = 0
Using the quadratic formula
That's
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
From the question
a = 4 , b = 16 , c = 25
Substitute the values into the above formula and solve
We have
[tex]x=\dfrac{-16\pm\sqrt{16^2-4(4)(25)} }{2(4)}[/tex]
[tex]x=\dfrac{-16\pm\sqrt{256-400} }{8}[/tex]
[tex]x=\dfrac{-16\pm\sqrt{-144} }{8}[/tex]
[tex]x=\dfrac{-16\pm12 \ i}{8}[/tex]
Separate the real and imaginary parts
That's
[tex]x=\dfrac{-16}{8}\pm\dfrac{12}{8} \ i[/tex]
[tex]x=-2\pm\dfrac{3}{2} \ i[/tex]
We have the final answer as
[tex]x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i[/tex]
Hope this helps you
Find the equation of a line that passes through the points (1,3) and (2,2). Leave your answer in the form
y
=
m
x
+
c
The equation of the line that passes through the points (1,3) and (2,2) is y = -x + 4.
To find the equation of the line, we can use the slope-intercept form of a linear equation, y = mx + c, where m is the slope and c is the y-intercept.
First, we need to find the slope of the line. The slope is given by:
m = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two given points. Plugging in the values, we get:
m = (2 - 3)/(2 - 1) = -1Next, we can use one of the given points and the slope to find the y-intercept. Using the point (1,3), we get:
3 = (-1)(1) + cSimplifying this equation gives us:
c = 4
Therefore, the equation of the line in slope-intercept form is:
y = -x + 4.
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Weight: 20kg Order: 10 mg q6 hours Therapeutic range : 2-3 mg/kg/day. What is daily dose? Is it safe? Is it therapeutic?
The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.
The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.
=> (10mg x 4 doses) = 40 mg
The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.
However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.
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how many legs does it take to make 109657 spiders
Assuming each spider has 8 legs, it would take 877,256 legs to make 109,657 spiders
7. Select all expressions which give the measure of angle A.
(A.) arccos (28/53)
(B.) arccos (45/53)
(C.) arcsin (28/53)
(D.) arcsin (45/53)
(E.) arctan (28/45)
(F.) arctan (45/28)
We cannot use arccos (28/53) and arcsin (28/53) because they correspond to angle B, not angle A. Similarly, arctan (28/45) and arctan (45/28) do not give the measure of angle A.
What accomplishes arccos function?The cosine function has an opposite known as the arccos function. It provides the angle whose cosine is the specified value. Try it. Drag any vertex of the triangle and watch how the angle C is determined using the arccos() function. Meaning: A 30 degree angle is one whose cosine is 0.866.
What is the sine of two?The inverse cosine function is the arccosine. The arccosine function's input values range from -1 to 1, matching the cosine function's output range of -1 to 1. So, for x=2, arccos x is undefined.
From the given figure, we can see that:
cos A = 28/53
sin A = 45/53
Therefore, the expressions that give the measure of angle A are:
(B.) arccos (45/53)
(D.) arcsin (45/53)
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A rectangle has vertices at (-2, 1), (3, 1). (3,-2), and (-2,-2).
What is the area of the rectangle?
Check the picture below.