Answer:
To factorize the quadratic expression f² + 7f + 10, we need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5. So, we can write:
f² + 7f + 10 = (f + 2)(f + 5)
Therefore, the answer is (f + 2)(f + 5).
Answer:
Step-by-step explanation:
[tex]f^2+7f+10=f^2+2f+5f+10=f(f+2)+5(f+2)=(f+5)(f+2)[/tex]
By grouping, we can factor the polynomial. We know that 2+5=7 and 2*5=10, so this is why (f+5) and (f+2) are factors of f²+7f+10.
6. suppose that a brand of aa batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. assume that when this milestone occurs follows a normal distribution (a) calculate the probability that a battery does not reach this milestone in its first 8 hours of usage. (b) suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until after 7.5 hours of usage. if n12, what is the probability of this goal being met? (c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.
The smallest number of batteries in the package for the probability to exceed 1% is a) 17. This can be calculated using the binomial distribution with parameters n=17 and b)p=0.2927 and number of batteries is c)4. (Where p is the probability from part a).
a) The probability that a battery does not reach the significant milestone after 8 hours of usage is 0.2927.
This can be calculated using the cumulative normal distribution function. The parameters are μ=7.36, σ=0.29, and x=8.
b) The probability that at least 10 batteries will last more than 7.5 hours is 0.7012.
This can be calculated using the binomial distribution with parameters n=12 and p=0.2927 (where p is the probability from part a).
c) The number of batteries should be in package is μ*4.2/7.5 = 4.
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What is a formula for the nth term of the given sequence? 24 , 36 , 54
The formula for the nth term of the series will be (11+n)*(n+1).
What is series?A series in mathematics is essentially the process of adding an infinite number of quantities, one after the other, to a specified starting quantity. A significant component of calculus and its extension, mathematical analysis, is the study of series. The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, whereas a sequence is an ordered group of elements in which repeats of any kind are permitted. One of the typical instances of a series or a sequence is an arithmetic progression.
In this the pattern of the series is
24=12*2
39=13*3
54=14*4
hence The formula for the nth term of the series will be (11+n)*(n+1).
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Pls solve 60 points if you do
Answer:
Cos2a - cot2a/sin2a - tan2a
Step-by-step explanation:
3. Find the distance from A to B. A(-2,2) B (4,-2)
The distance from points A(-2, 2) to B (4, -2) is equal to √52 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (-2 - 2)²]
Distance = √[(6)² + (-4)²]
Distance = √(36 + 16)
Distance = √52 units.
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Amir drove from Jerusalem to the lowest place on Earth, the Dead Sea.
His altitude relative to sea level (in meters) as a function of time (in minutes) is graphed.
How long did it take Amir to reach sea level?
In order to solve this problem, we need to begin by examining the graph of Amir's altitude relative to sea level. We can see that the graph starts at an altitude of 700 meters and ends at an altitude of 400 meters.
We can also see that the slope of the graph is negative, which means that the altitude is decreasing over time. This means that it will take Amir some amount of time to reach sea level (which is 0 meters).
To calculate how long it took Amir to reach sea level, we can use the following equation:
Time = (Altitude Final - Altitude Initial) / (Rate of Change)
In this equation, the Rate of Change is the slope of the graph, which can be determined by examining the graph.
Plugging in our values, we get:
Time = (400 - 700) / (-6) = 100 / (-6) = -16.67 minutes
Therefore, it took Amir 16.67 minutes to reach sea level.
if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
Landon buys cookies and lemons at the store he pays a total of $29.12 He pays $2.66 for the cookies he by seven bags of lemons that each cost the same amount Which tape diagram could be used to represent the contacts if X represents how much each bag of lemons cost
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
what is unitary method ?A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.
given
The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.
The first segment on the left, which is $2.66, represents the price of the cookies.
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
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Given the equation negative 24 equals y over 8, solve for y.
Answer: y = -192
Step-by-step explanation:
The equation given is:
-24 = y/8
To solve for y, we need to isolate the variable y on one side of the equation. We can do this by multiplying both sides by 8:
-24 x 8 = y
Simplifying the left side:
-192 = y
Therefore, the solution is y = -192.
I travel 480 km in 4 hours what is my speed in km/h
Answer:
120 km/h.
Step-by-step explanation:
480 km / 4h
Divide top and bottom by 4 to get the desired km/h.
We have 120 km/h.
Hope this helps!
(1 point) a bowl contains 6 red balls and 7 blue balls. a woman selects 4 balls at random from the bowl. how many different selections are possible if at least 3 balls must be blue?
The number of different selections possible if at least 3 balls must be blue is 35
1. Calculate the total number of possible selections (6 red + 7 blue = 13 total): 13C4 = 715
2. Calculate the number of possible selections that have fewer than 3 blue balls: 6C4 = 15
3. Subtract the number of possible selections with fewer than 3 blue balls from the total number of possible selections: 715 - 15 = 700
4. Divide the answer by the number of selections with exactly 3 blue balls: 700/7 = 100
5. Multiply the result by the number of selections with exactly 4 blue balls: 100 * 7 = 700
6. Finally, subtract the number of selections with 4 blue balls from the total number of possible selections: 715 - 700 = 35
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Brian can paint a room in 3 hours. Latoya can paint the same room in 2 hours and 15 minutes. How long would it take them if they worked together.
Answer: 45min
Step-by-step explanation:
3x60=180
2x60=120
120+15=135min
180-135=45min
Please help me with my math!
Answer:
35 passengers produce the maximum revenue for the bus company.
Step-by-step explanation:
Define the variables:
Let "x" be the total number of passengers.Let "y" be the total revenue of the bus company (in dollars).If there are 30 or fewer passengers, each passenger will be charged $80. Therefore, the equation for the total revenue for 30 or fewer passengers is:
[tex]y = 80x,\quad x \leq 30[/tex]
If there are more than 30 passengers, each passenger will be charged $80 minus $2 for every passenger over 30. Therefore, the equation for the total revenue for more than 30 passengers is:
[tex]y = [80 - 2(x - 30)]x, \quad x > 30[/tex]
This simplifies to:
[tex]y = [80 - 2x + 60]x, \quad x > 30[/tex]
[tex]y = [140 - 2x]x, \quad x > 30[/tex]
[tex]y = 140x - 2x^2, \quad x > 30[/tex]
To maximize revenue, we need to find the value of x that maximizes the above equation.
Since this is a quadratic function, the maximum value occurs at the vertex of the parabola.
The x-value of the vertex of a parabola in the form y = ax² + bx + c is when x = - b/2a. Therefore, the x-value of the vertex is:
[tex]\implies x_{\sf vertex}=\dfrac{-140}{2(-2)}=\dfrac{-140}{-4}=35[/tex]
Therefore, the number of passengers that produce the maximum revenue for the bus company is 35.
Construct triange ABC, in which AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. Measure the length of BC. Give your answer to 1 d. P
From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm
To construct triangle ABC, we can follow these steps:
Draw a line segment AB of length 6 cm.Draw an angle of 96 degrees at point A using a protractor.Draw an angle of 35 degrees at point B using a protractor.The intersection point of the two lines that were drawn in step 2 and 3 will be point C, which is the third vertex of the triangle.To measure the length of BC in triangle ABC, we can use the law of sines.
The law of sines states that in any triangle ABC:
a / sin(A) = b / sin(B) = c / sin(C)
Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.
In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:
angle ACB = 180 - angle BAC - angle ABC
= 180 - 96 - 35 = 49 degrees
Now, we can apply the law of sines to find the length of BC:
BC / sin(35) = 6 / sin(96)
BC = 6 × sin(35) / sin(96)
Using a calculator, we can evaluate this expression to get:
BC ≈ 4.22 cm
Therefore, the length of BC in triangle ABC is approximately 4.22 cm.
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show that a strictly diagonally dominant matrix is invertible. show furthermore that if all the diagonal entries are positive, then all the eigenvalues have positive real part.
Completing the proof that if A has strictly positive diagonal entries, then all of its eigenvalues have a positive real part.
For any square matrix A, a diagonal element is any element that is on the main diagonal, i.e., (i,i) for 1<=i<=n. If A has strictly diagonal dominance, then for each row i of A, the absolute value of the diagonal element of that row is more than the sum of the absolute values of the non-diagonal elements of that row.If A is invertible, then det(A) is nonzero. If all the diagonal entries are positive, then det(A) is also positive, which implies that all the eigenvalues of A have the same sign (either all are positive or all are negative).As a result, suppose all of A's diagonal entries are positive. Then all of A's eigenvalues are positive since they all have the same sign as det(A).
And if all of A's eigenvalues are positive, then all of their real parts are positive as well, hence completing the proof that if A has strictly positive diagonal entries, then all of its eigenvalues have a positive real part.
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Find dy/dx if y=u^3 + 2u and u= x^2 + 5
Answer: I hope this helped!
Step-by-step explanation:
.
A bag of oranges weighs 1.5 kg to the nearest 100 g. Complete the error interval, where x is the weight of the oranges.
The ratio of shirts to pants is 3 to 2. If there are 6 shirts, how many pants are there?
12
6
4
9
A survey was given to a random sample of 1050 voters in the United States to ask about their preference for a presidential candidate. Of those surveyed, 693 respondents said that they preferred Candidate A. Determine a 95% confidence interval for the proportion of people who prefer Candidate A, rounding values to the nearest thousandth
As per the confidence interval, the true proportion of people in the population who prefer Candidate A lies somewhere between 0.622 and 0.698, based on the results of the survey of 1050 voters.
To calculate the margin of error, we will use the following formula:
Margin of error = z x standard error
Where z is the critical value from the standard normal distribution corresponding to our desired confidence level (95%), and the standard error is given by:
Standard error = √[(sample proportion x (1 - sample proportion)) / sample size]
Using a z-table, we find that the critical value for a 95% confidence interval is 1.96
Plugging in the values we have, we get:
Standard error = √[(0.66 x 0.34) / 1050] = 0.0193
Margin of error = 1.96 x 0.0193 = 0.0378
Therefore, the 95% confidence interval for the proportion of people who prefer Candidate A is:
0.66 ± 0.0378
Rounded to the nearest thousandth, the lower bound of the confidence interval is 0.622 and the upper bound is 0.698.
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Solve
2n > 20
Pls help really quick
Answer:
n > 10
Step-by-step explanation:
2n > 20
2n/2 > 20/2
n > 10
A person buys a bike for $360. He pays 60% of the cost price and then pays $15 over a period of 12 months. How much did he pay in total?
Answer: The person paid $396.
Step-by-step explanation:
1. Since we need to find 60% of 360, we can do 360 x 60/100.
2. We are now left with 216.
3. Now we have to add the total together.
4. 216 + (15x12) = 396.
5. The person paid $396.
A student has 30 minutes to complete an exam. There are 9 multiple choice questions worth 3 points each. There are also 3 short answer questions worth 5 points each. It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question. How many multiple choice questions and short answer questions should the student answer to maximize his score in the time remaining (Use x = multiple choice; y = short answer.)State the Objective Function (S for score) in the linear programming problem givenA. S = 5x + 3y B. S = 3x + 5y C. S = 2x + 6y D. S = 6y + 2x
The Objective Function in the linear programming problem given in the above-stated scenario is:
B. S = 3x + 5y
Linear programming is a statistical technique used to find a maximum or minimum value of an equation in order to find a solution to a problem. It is used to calculate how much to produce to maximize profits, how to allocate resources, and determine which investments to make.
Linear programming problems include an objective function, which is the equation to be maximized or minimized, and constraints that must be followed. Linear programming problems can be solved graphically or algebraically. In order to solve a linear programming problem, we first need to identify the objective function and constraints.
Objective Function in the linear programming problem:
The score of the student is to be maximized in the given time frame by answering the maximum number of questions of both types.
Therefore, the objective function is: S = 3x + 5y
Answer: B. S = 3x + 5y
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Which of the expressions below are equal to 8? Select all that apply. A) 2 + 2 + 2 + 2 B) 4 x 2 C) 1 x 8 D) 8 + 8 E) 4 + 4 + 4 + 4
Answer:
A ,B ,C
Step-by-step explanation:
2+2+2+2 equals 8
4x2 equals 8 and
1x8 equals 8
Answer:
A) 2 + 2 + 2 + 2
B) 4 × 2
C) 1 × 8
Hope this helps!
Step-by-step explanation:
A = 4 + 4 = 8
B = 8
C = 8
D = 16
E = 16
To compare the pain control offered by two different analgesics in pediatric patients, the authors selected the Wong-Baker FACES pain rating scale as the primary end point. Before beginning the clinical trial, the authors sought to validate this ordinal scale by showing a correlation with a previously validated visual analog scale. Which one of the following statistical test is most appropriate to assess whether a correlation exists between these two measurements?
A. Pearson correlation
B. Analysis of variance (ANOVA)
C. Spearman rank correlation
D. Regression analysis
The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.
What is correlation?Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.
Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".
The formula for Spearman's rank correlation coefficient:
Rs = 1 - {6Σd₂}/{n(n₂-1)}
Where, Σd₂ = the sum of the squared differences between ranks.
n = sample size
Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.
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HELP ILL GIVE BRAINLY THINGY AND 100 POINTS
Answer is X=2.
1. Collect like terms
(x) + 4 + 9 = 17 - x
2. Add the numbers
x + (13) = 17 - x
3. Move the variable to the left-hand side and change its sign
x + 13 (+x) = 17
Move the constant to the right-hand side and change its sign
x + x = 17 - 13
4. Collect like terms
2x = 17 - 13
Subtract the numbers
2x = 4
5. Divide both sides of the equation by 2
Therefore, you get your solution: X=2.
Using the properties of equality, the steps for solving the equation is explained below.
How to Solve an Equation Using the Properties of Equalities?To solve an equation, we would apply the properties of equalities where necessary to isolate the variable in the equation to one side.
Step 1: [tex]3x + 4 - 2x + 9 = 17 - x[/tex] [given]
Step 2: [tex]x + 13 = 17 - x[/tex] [Combine like terms]
Step 3: Add x to both sides of the equation
[tex]x + 13 + x = 17 - x + x[/tex] [addition property of equality]
Step 4: [tex]2x + 13 = 17[/tex] [simplify]
Step 5: Subtract 13 from both sides
[tex]2x + 13 - 13 = 17 - 13[/tex] [subtraction property of equality]
Step 6: [tex]2x = 4[/tex] [simplify]
Step 7: [tex]x = 2[/tex] [division property of equality]
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Simplify the expression.
n+ 3(n − 1) =
Kaitlin is on vacation at a tropical bay that has three islands. She rents a boat on Island A and plans to navigate to Island C, which is 13 miles away. Based on the figure below, at what angle should she navigate to go to Island C?
She should navigate at angle 76.86° to go to Island C.
How to find the angle for navigation?The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:
cosA = (b² + c² - a²)/2bc
where a, b and c are the lengths and A, B and C are the angles for the islands respectively
Using the formula:
cosA = (b² + c² - a²)/2bc
cosA = (13² + 11² - 15²)/(2*13*11)
cosA = 5/22
A = arc cos(5/22)
A = 76.86°
Thus, θ = 76.86
Therefore, she should navigate at angle 76.86° to go to Island C.
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divide 210 kg of suger in the ratio 1:2
Answer: 105:210
Step-by-step explanation:
1:2 = ?:210
? = 210/2 = 105
1:2 = 105:210
a card is drawn randomly from a standard 52-card deck. find the probability of the given event. write your answers as reduced fractions or whole numbers.
The probability of the given event is 11/13.
How to find the probabilityA card is drawn randomly from a deck of 52 cards.
The probability that the card drawn is neither an ace nor a king is a question that can be answered with probability.
We know that there are 4 aces and 4 kings in a deck of 52 cards.
The probability of drawing an ace or a king is P(Ace or King) = 4/52 + 4/52 = 8/52 = 2/13
There are four of each card rank in a deck of 52 cards, and there are a total of 52 cards. A player must choose one of the 52 cards at random.
The probability of drawing an ace or a king is P(Ace or King) = 4/52 + 4/52 = 8/52 = 2/13
The probability of at drawing neither an ace nor a king is:
P(Not Ace and Not King) = 1 - P(Ace or King) = 1 - 2/13 = 11/13
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Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 *Explain your answer (2pt cach) a. 20, 24, 21, 19, 18 b. 20, 20, 20, 20, 20
The two options are as follows: a. 20, 24, 21, 19, 18.
This sample is a possible bootstrap sample.
A bootstrap sample is created by taking samples from the original sample with replacement. Therefore, we can include the original data multiple times.
Here, 20, 24, 19, 23, 18 is the original sample.
Sample a includes 20, 24, 19, 23, and 18 which are part of the original data, and 21 which is not part of the original data. Since we can include the original data multiple times in bootstrap samples, a is possible.b. 20, 20, 20, 20, 20This sample is not a possible bootstrap sample.
In the original sample, we have five unique data points: 20, 24, 19, 23, and 18. Sample b includes only one unique data point, 20, repeated five times. We cannot create a bootstrap sample with the same data point repeated multiple times. Hence A is correct.
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Which equations arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers? (123, 2347) (Check all that apply.) Check All That Apply 1 = 10 - 3.3 1 = 37.10 - 3. 123 1 = 37.2347-706 - 123 1 = 37.10 -9.41 d d 1 = 36.2347-583 123
The equations that arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:
1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.
What is the Euclidean algorithm?The Euclidean algorithm is a recursive method for finding the greatest common divisor (GCD) of two positive integers. When we divide the larger number by the smaller number, we obtain the remainder. The smaller number and the remainder are then passed on as input to the next round. The process continues until the remainder is zero, at which point the GCD is obtained.
The solution to the given problem is as follows:
We will use the Euclidean algorithm to compute gcd(123, 2347).
123 ÷ 2347 = 0 remainder 123.2347 ÷ 123 = 19 remainder 106.123 ÷ 106 = 1 remainder 17.106 ÷ 17 = 6 remainder 4.17 ÷ 4 = 4 remainder 1.4 ÷ 1 = 4 remainder 0.The last nonzero remainder we get is 1.
Therefore, the greatest common divisor (GCD)(123, 2347) = 1.
The greatest common divisor of 123 and 2347 can be expressed as a linear combination of the two numbers in the following ways:1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.
Thus, the equations arising when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:
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