By using addition calculation, we determine that Angela will end up making 42 cards in total.
Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.
So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:
23 + 19 = 42
Therefore, Angela will make 42 cards in all.
By using simple arithmetic calculation of basic addition, we find that Angela will make 42 cards in all.
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What’s the area?
7 yd
4 yd
7 yd
3 yd
The area is 49 square yards.
What is the quotient of 6. 208 × 10^9 and 9. 7 × 10^4 expressed in scientific notation?
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
Quotient:
The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.
Based on the given conditions, Formulate:
6.208× 10⁹ /9.7×10⁴
Simply using exponent rule with same base:
[tex]a^n. a^m = a^(n+m)[/tex]
= 6.208 × 1/9.7
Now,
the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³
Now solving, we get:
6.208/9.7 × 10¹³
Converting fraction into decimal, we get:
0.64× 10¹³
⇒ 6.4 × 10¹²
Therefore,
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
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Find the tangential and normal components of the acceleration vector for the curve → r ( t ) = 〈 − 3 t , − 5 t ^ 2 , − 2 t ^ 4 〉 at the point t = 1
The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459
How do we calculate the tangential component?The acceleration vector can be found from the following formula:
[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]
To find the tangential component of the acceleration vector, we first need the velocity vector v(t).
[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]
Next, we need to normalize the velocity vector using the following formula:
[tex]T(t) = v(t) / ||v(t)||,[/tex]
Where ||v(t)|| is the magnitude of the velocity vector.
[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]
Then, the tangential component of a(1) is:
[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]
How do we calculate the normal component?To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.
[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)} = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]
Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:
[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]
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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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A ball is thrown upward with an initial velocity of 75 feet per second and an initial height of 4 feet. Given h(t) = −16t2 + v0t + h0, complete function h to model the vertical motion of the ball. Then find the ball’s maximum height, to the nearest foot.
h(t) = −16t2 + ? t + ?
maximum height:
The ball reaches a maximum height of approximately 146 feet, to the nearest foot.
What exactly does the term Maximus height mean?Maximum Height refers to the highest point of the structure or sign as measured from the average natural ground level at the base of the supporting structure.
The ball is thrown upward with an initial velocity of 75 feet per second, implying that v0 = 75. We are also told that the ball is thrown from a height of 4 feet, implying that h0 = 4.
The function: can be used to model the ball's vertical motion.
16t2 + v0t + h0 = h(t).
Substituting v0 and h0 values yields:
h(t) = -16t^2 + 75t + 4
To determine the maximum height of the ball, we must first locate the vertex of the parabolic function h. (t). The vertex of the parabola is given by the equation y = ax2 + bx + c:
x = -b / 2a
y = c - b^2 / 4a
a = -16, b = 75, and c = 4 in this case. Substituting these values into the above formulas yields:
t = -75 / 2(-16) = 2.34 sec
h(t) = 4 - (752) / (4(-16)) 146 ft.
As a result, the ball reaches a maximum height of about 146 feet to the nearest foot.
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True or false (with a counterexample if false)?(a) The vectors that are not in the column space form a subspace.(b) If contains only the zero vector, then is the zero matrix.(c) The column space of equals the column space of .(d) The column space of equals the column space of .
(a) False; A subspace is formed by the set of vectors that do not belong to the column space.
(b) True; If the matrix contains solely the zero vector, then it is the zero matrix.
(c) True; The column space of a particular matrix is equivalent to the column space of another specified matrix.
(d) False; The column space of one matrix is identical to the column space of another matrix.
(a) False; if A = [1 0; 0 0], then the column space of A is { e1 }, where e1 is the standard unit vector in the plane. If v is not in the column space of A, but w is not in the column space of A, then v + w is not in the column space of A.
Therefore, the set of vectors that are not in the column space of A does not form a subspace.
(b) True; if every vector in Rn is in the null space of A, then in particular, every standard unit vector is in the null space of A. Thus, the ith column of A is zero for i = 1, . . . , n, so A is the zero matrix.
(c) True; the column space of A is generated by the columns of A, while the column space of AB is generated by linear combinations of the columns of AB. By definition of matrix multiplication, the columns of AB are linear combinations of the columns of A, so the column space of AB is a subspace of the column space of A. Conversely, let b be in the column space of A. Then there is an x in Rm such that Ax = b. Thus, ABx = A(Bx), so b is in the column space of AB. Therefore, the column space of A is a subspace of the column space of AB. Hence the two column spaces are equal.
(d) False; if A = [1 0; 0 0] and B = [0 0; 0 1], then the column space of A is { e1 }, while the column space of B is { e2 }. The column space of AB is { 0 }, so it is not equal to either column space.
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c) assume that 25% of the defendants in the state are innocent. in a certain year 200 people put on trial. what is the expected value and variance of the number of cases in which juries got the right decision?
The expected value of cases in which juries got the right decision is 150, and the variance is 375.
1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.
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cosθ(1+tanθ)=cosθ+sinθ
Answer:
Starting with the left side of the equation:
cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)
= cosθ + sinθ
Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.
Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
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Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
16 ft
Find the area.
20 ft
12 ft
10 ft
15 ft A = [?] ft²
Round to the nearest
hundredth.
then the area would be: [tex]Area=\frac{(a+b)}{2*h}[/tex] = (16 ft + 10 ft)/2 x 15 ft = 150 ft²
What is area?Area is a mathematical term that refers to the measurement of the size or extent of a two-dimensional region or surface. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²). The area of a shape is determined by multiplying the length and width of the shape in the case of a rectangle or square, or by using more complex formulas for irregular shapes such as circles, triangles, or polygons. The concept of area is important in various fields such as mathematics, geometry, physics, engineering, and architecture, among others.
by the question.
. If we assume that these are the dimensions of a rectangle, then the area would be:
Area = length x width = 20 ft x 12 ft = 240 ft²
However, if we assume that the area is a trapezoid with a height of 15 ft, and the parallel sides of length 16 ft and 10 ft.
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I need help with answer this question
Answer:
y = 2x/15 + 6
Step-by-step explanation:
3y/2 = x/5 + 9
3y = (x/5 + 9) (2) The 2 that was dividing goes on to multiply on the other side.
3y= 2x/5 + 18
y = (2x/5 + 18) / 3 The 3 that was multiplying goes on to divide on the other side.
y = 2x/15 + 6
Whats 21 square root of 98 divided by 7 square root of 21
The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407
A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.
Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.
Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.
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parabola a and parabola b both have the x-axis as the directrix. parabola a has its focus at (3,2) and parabola b has its focus at (5,4). select all true statements.
a. parabola A is wider than parabola B
b. parabola B is wider than parabola A
c. the parabolas have the same line of symmetry
d. the line of symmetry of parabola A is to the right of that of parabola B
e. the line of symmetry of parabola B is to the right of that of parabola A
In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.
The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.
Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.
Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.
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=
Suppose that a new employee starts working at $7.32 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y = $7.32(1.04). Find
the amount of time after which he will be earning $10.00 per hour.
After what amount of time will the employee be earning $10.00 per hour?
years (Round to the nearest tenth of a year as needed.)
HELP PLEASE
Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
We can start by setting up the equation for the employee's hourly wage y after t years -
[tex]y = $7.32(1.04)^t[/tex]
We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -
[tex]10 = $7.32(1.04)^t[/tex]
Dividing both sides by $7.32, we get -
[tex]1.367 = 1.04^t[/tex]
Taking the natural logarithm of both sides, we get -
[tex]ln(1.367) = ln(1.04^t)[/tex]
Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -
ln(1.367) = t ln(1.04)
Dividing both sides by ln(1.04), we get -
t = ln(1.367)/ln(1.04) ≈ 9.64
Therefore, the employee will be earning $10.00 per hour after about 9.64 years.
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What is the difference between the simple and compound interest if you borrow $3,000 at a 6% interest rate for 2 years?
$180.00
$10.00
$6.00
$80.00
Answer:
Correct option is C)
Simple interest =
100
3000×6×2
=360
Compound interest =3000(1+
100
6
)
2
−3000=18×20.6=370.8
∴ Difference is Rs.10.8.
you can convert this value to $$
or simply the answer will be 2. $10
(hob-evzw-zjw) come
Answer:
B is your answer.
10.80$ which you just round to 10. 10 is your answer.
Step-by-step explanation:
For simple interest, the formula is:
Simple Interest = Principal × Rate × Time
For compound interest, the formula is:
Compound Interest = Principal × (1 + Rate)^Time - Principal
Let's calculate the values:
Principal = $3,000
Rate = 6% or 0.06
Time = 2 years
Simple Interest = $3,000 × 0.06 × 2 = $360
To calculate compound interest, we need to use the formula:
Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000
= $3,000 × (1.06)^2 - $3,000
= $3,000 × 1.1236 - $3,000
= $3,370.80 - $3,000
= $370.80
The difference between simple and compound interest is:
$370.80 - $360 = $10.80
what is the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 ? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378
First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.
The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.
The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).
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X is a Poisson RV with parameter 4. Y is a Poisson RV with parameter 5. X and Y are independent. What is the distribution of X+Y? A. X+Y is an exponential RV with parameter 9 B. X+Y is a Poisson RV with parameter 4.5 C. X+Y is a Poisson RV with parameter 9
The distribution of C) X+Y is a Poisson RV with parameter 9.
This is because the sum of two independent Poisson distributions with parameters λ1 and λ2 is also a Poisson distribution with parameter λ1 + λ2. Therefore, X+Y follows a Poisson distribution with parameter 4+5 = 9.
Option A is incorrect because an exponential distribution cannot arise from the sum of two Poisson distributions. Option B is also incorrect because the parameter of X+Y is not the average of the parameters of X and Y. Option C is the correct answer as explained above.
In summary, the distribution of X+Y is Poisson with parameter 9.
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Each angle of a regular polygon is 1680. How
many sides has it? What is the name of this
polygon?
Answer: 2 solutions
Step-by-step explanation:
To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)
Setting them equal, we get (180n-360)/n = 1680.
Multiplying by n on both sides, we get 180n-360 = 1680n.
Solving, we get 1500n = 360.
n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.
The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.
Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.
Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.
Find the first 4 terms of the sequence represented by the expression 3n + 5
The first 4 terms of the sequence represented by the expression 3n + 5
is 8, 11, 14 and 17.
Sequence:
In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.
According to the Question:
Given, aₙ = (3n+5).
First four terms can be obtained by putting n=1,2,3,4
a 1=(3×1+5) = 8
a 2 =(3×2+5) = 11
a 3 =(3×3+5) = 14
a 4 =(3×4+5) = 17
First 4 terms in the sequence are 8, 11, 14, 17.
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A dolphin was swimming 6 feet below sea level. The number line shows the
location of the dolphin. It then swam down 3 feet. Describe how to use the
number line to find the new location of the dolphin.
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
OA. On the number line, move 3 units to the left. End at -9. The dolphin
was 9 feet below sea levelsm
OB. On the number line, move 3 units to the right. End at 9. The dolphin
was 9 feet above sea level.
OC. On the number line, move 3 units to the left. End at 3. The dolphin
was 3 feet above sea level.
OD. On the number line, move 3 units to the right. End at -3. The
dolphin was 3 feet below sea level.
On the number line, move 3 units to the left. End at -9. The dolphin was 9 feet below sea level.
What is location?
Location refers to the specific position or coordinates of an object or point in space or time. It can refer to the physical location of an object or place on Earth, such as a building or city, or the position of an astronomical object in the universe.
In a mathematical context, location is often expressed as a set of coordinates or points in a coordinate system.
Location is an important concept in various fields, including geography, cartography, astronomy, and mathematics, and is often used to describe and locate objects, places, or events in a precise and accurate manner.
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a pastry chef accidentally inoculated a cream pie with six s. aureus cells. if s. aureus has a generation time of 60 minutes, how many cells would be in the cream pie after 7 hours?
After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.
How many cells would be in the cream pie after 7 hours?Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.
The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.
If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.
The number of generations (n) in seven hours is calculated as:
n = t/g
n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations
The number of cells in the cream pie after 7 hours is calculated as :
N = N₀ × 2ⁿ
N = 6 cells × 2⁷
N = 768 cells
Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.
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Levi's investment account accrues interest biannually. The function below represents the amount of money in his account if the account is left untouched for
t years.
f(t) = 2000 (1.03)2t
The amount of money in the account ( increases or decreases )
by (2 , 3 or 103)
% (every six months, each year, or every two years)
Answer:
The amount of money in the account increases by 3% every six months, or biannually.
To see why, we can break down the function f(t) = 2000(1.03)^(2t):
The base amount in the account is $2000.The term (1.03)^(2t) represents the interest accrued over time.Since the interest is compounded biannually, the exponent of 2t indicates the number of six-month periods that have elapsed. For example, if t = 1, then 2t = 2, which means two six-month periods have elapsed (i.e., one year).
Each time 2t increases by 2, the base amount is multiplied by (1.03)^2, which represents the interest accrued over the two six-month periods.
Thus, the amount of money in the account increases by 3% every six months, or biannually.
As for the second part of the question, the amount of increase is not 2%, 3%, or 103%.
F(x)=-(x+3)(x+10) pls help
Answer:
Zeros: x = -10 and x = -3
Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]
Step-by-step explanation:
Pre-SolvingWe are given the following function:
f(x) = -(x+3)(x+10)
We want to find the zeros and the vertex of the parabola.
SolvingZerosThe zeros are the values of the function where f(x) = 0.
So, in order to find the zeros, we can set f(x) = 0.
0 = -(x+3)(x+10)
We can divide both sides by -1, to get:
0 = (x+3)(x+10)
To solve this, we will use zero product property.
Split and solve:
x+3 = 0
x = -3
x+10=0
x = -10
Vertex
Now, to find the vertex, we first get the average of the zeros.
Add the values of the zeros together, then divide by two:
[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]
Now, we plug this in for x to get the y value (found through f(x)) of the vertex.
[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]
So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]
Can someone help me with this please?
To solve the question asked, you can say: So, the other angle of the figure is 49 degree.
what are angles?In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.
here the given angles are as -
107 + (180-156) + x = 180
as total angle sum of a triangle is 180
so,
x = 180 - 131
x = 49
So, the other angle of the figure is 49 degree.
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HELPPPPPPP PLEASEEEEEEEEEEEEEEE
y=mx+b
The required equation of straight line is y = 0.03x + 20.
What is an equation?
A mathematical equation states that two quantities or values are identical. Equations are used when more than one factor has to be examined in order to fully understand or explain a situation.
The general form of an equation is y = mx + b, where m is the slope of equation and b is a constant.
From the given graph we get 2 points.
i.e., (0, 20) and (2000, 80)
Slope of the line is
[tex]m=\frac{80-20}{2000-0}\\\ \ = \frac{60}{2000}\\ = \frac{6}{200} \\= \frac{3}{100}[/tex]
Then the equation will be
[tex]y-20=\frac{3}{100}(x-0)\\\Rightarrow y-20=0.03x\\\Rightarrow y-0.03x-20=0\\\Rightarrow y = 0.03x+20[/tex]
Therefore, the required equation is y = 0.03x + 20, calculating with the help of given graph.
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If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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Two percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 95% detection rate for carriers and a 3% detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual. A. What is the probability that both tests yield the same result?
The probability that both tests yield the same result is 7.7%.
Simply put, probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
It is predicated on the likelihood that something will occur. The justification for probability serves as the primary foundation for theoretical probability. For instance, the theoretical chance of receiving a head when tossing a coin is 12.
Let's break it down:-
90% don't have of those 99%
5% will be positive
1% positive of those 1%
90% positive
10% negative.
Well we need it to be the same, so 99*(.05*.05+.95*.95)+.01*(.9*.9+.1*.1)= 90.4%.
If both tests are positive, we have:-
0.99*0.05*0.05 and 0.01*0.9*0.9 for being positive, so :-
[tex]\frac{carrier}{positive} = \frac{0.01*0.9*0.9}{(0.99*0.05*0.05+0.01*0.9*0.9)} = 7.7[/tex]
hence, the probability of the two tests yield the same result is 7.7%.
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A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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If you run towards a faraway friend at 5 miles per hour and she bikes towards you at 15 miles per hour, how many miles closer are you to each other after 1 hour?
Using the unitary method we calculate that the friend would be 20 miles closer in an hour.
If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:
5 miles / hour - (- 15 miles / hour) = 20 miles / hour
Also, we know that
speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,
20 miles/hour × 1 hour = 20 miles
Therefore, you would be 20 miles closer to each other after 1 hour.
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