Option D. 12x + 6y = 10, -4x - 6y = -16. To eliminate y from the system of equations, we need to multiply one or both equations by a constant so that the coefficients of y have opposite signs.
Then we can add or subtract the equations to eliminate y.
We can do this by multiplying one or both equations by a constant that will make the coefficients of y add to zero. The goal is to create additive inverses of the coefficients of y in the two equations.
Looking at the two equations:
12x + 6y = 10
2x + 3y = 8
We can see that the coefficients of y are 6 and 3. To eliminate y, we need to find a common multiple of 6 and 3 that will make the coefficients of y additive inverses of each other. The least common multiple of 6 and 3 is 6, so we can multiply the second equation by -2 to get:
-4x - 6y = -16
Now we can add this equation to the first equation to eliminate y:
12x + 6y = 10
(-4x - 6y = -16)
8x = -6
Therefore, the correct pair of equations after multiplying to eliminate y is:
12x + 6y = 10
-4x - 6y = -16
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i need help asap thanks
Answer:
im sure this isnt much help but i used desmos and i got the answer 0.5 w
Step-by-step explanation:
heres what i did on the calculator. i did what the screen shows it shows an adjacent(4) and the opposite(2) so therefor i did the obvious evaluation and thought oppostie over adjacent which is tangent formula by the way. so then i did tan(2/4) and got 0.008726867791 and then did what a video that i watched to refresh myself on this topic. so the video said that after that your supposed to do tan-1(0.00872687791) and then i got 0.5... not sure if that makes sense. i typed alot so ill just link the video for you to watch.
https://youtu.be/Rbxb6DOjarI
2 If Calvin scored a total 2,178 points in 11 games of bowling, what is Calvin's average per game?
Calvin's average score per game is 198.To find Calvin's average score per game, we need to divide the total points by the number of games played. Therefore, we can use the formula:
Average score per game = Total points / Number of games
Substituting the given values, we get:
Average score per game = 2,178 / 11
Simplifying the expression, we get:
Average score per game = 198
Therefore, Calvin's average score per game is 198. This means that over the course of 11 games, he scored an average of 198 points per game.
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Santa Claus has 3h+11 red presents and h+5 white presents in his stocking. Ethan selects a present at random from the stocking.
The value of h is 1.89. The solution involves setting up and solving an equation involving the probabilities of selecting a red or white present.
Santa Claus has a total of 3h+11 red presents and h+5 white presents in his stocking. If Ethan selects a present at random from the stocking, the probability of obtaining a red present is given as 19/26. Using this information, we can form an equation (3h+11)/(4h+16) = 19/26 and solve for h. Cross-multiplying and simplifying, we get 494h = 936, which leads to h = 1.89. Therefore, the value of h that satisfies the given conditions is approximately 1.89.
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Complete question:
Santa Claus has 3h+11 red presents and h+5 white presents in his stocking. Ethan selects a present at random from the stocking. Given that the probability that he obtains a red present is 19/26, find the value of h.
Many historians agree that there is about 1 chance in 4 that Jones wrote the ‘Q document’ and 3 chances in 4 that Smith wrote it. In a new analysis of the 10,000-word document, the word ‘that’ is found to occur 27 times. From the known writings of Smith and Jones, experts assess a probability of 0. 0084 that this frequency of ‘that’ would be observed if Jones were the author, whilst the probability for Smith would be 0. 4. In the light of this new evidence, what now is the probability that Jones is the author?
The probability of Jones being the author is 0.0275.
The new evidence updates the probability of Jones being the author from 1 in 4 to 0.0084. The probability of Smith being the author is 0.4.
To calculate the new probability, we need to use Bayes' theorem.
P(Jones|that) = P(that|Jones) x P(Jones) / (P(that|Jones) x P(Jones) + P(that|Smith) x P(Smith))
P(Jones|that) = 0.0084 x 0.25 / (0.0084 x 0.25 + 0.4 x 0.75)
P(Jones|that) = 0.0084 / (0.0084 + 0.3)
P(Jones|that) = 0.0084 / 0.3084
P(Jones|that) = 0.0275
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A chemical equation is given
below. How would you classify
this reaction?
4C5H₂O + 270220CO2 + 18H₂O
I need help solving these!
The simplification of the following equations will be:[tex]4\sqrt{3}\ \ 6\sqrt{2}\ \ 20\sqrt{3}\ \ 5\sqrt{5}\ \ 50\sqrt{3}\ \ 24\sqrt{2}\ \ 20\sqrt{7}\ \ 6\sqrt{15}\ \ 40\ \ 21\sqrt{2}\ \ 10\sqrt{11907}[/tex].
What are prime factors?Prime factorization is the process of transforming a number into a prime product. A prime number simply has the number itself and the number itself as its two components. The prime numbers, for instance, are 2, 3, 5, 7, 11, 13, and 19. Any integer can be expressed as the sum of prime integers thanks to prime factorization.
[tex]$\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4 \sqrt{3}$[/tex]
[tex]$\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6 \sqrt{2}$[/tex]
[tex]$\sqrt{1200} = \sqrt{400 \cdot 3} = \sqrt{400} \cdot \sqrt{3} = 20 \sqrt{3}$[/tex]
[tex]$\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5 \sqrt{5}$[/tex]
[tex]$\sqrt{98}$[/tex] 98 already has the simplest root form, since it does not have a perfect square factor.
[tex]$\sqrt{7500} = \sqrt{25 \cdot 300} = \sqrt{25} \cdot \sqrt{300} = 5 \sqrt{300} = 5 \sqrt{100 \cdot 3} = 5 \cdot 10 \sqrt{3} = 50 \sqrt{3}$[/tex]
[tex]$6 \sqrt{32} = 6 \sqrt{16 \cdot 2} = 6 \sqrt{16} \cdot \sqrt{2} = 6 \cdot 4 \sqrt{2} = 24 \sqrt{2}$[/tex]
[tex]$10 \sqrt{28} = 10 \sqrt{4 \cdot 7} = 10 \sqrt{4} \cdot \sqrt{7} = 20 \sqrt{7}$[/tex]
[tex]$3 \sqrt{60} = 3 \sqrt{4 \cdot 15} = 3 \sqrt{4} \cdot \sqrt{15} = 6 \sqrt{15}$[/tex]
[tex]$5 \sqrt{64} = 5 \cdot 8 = 40$[/tex]
[tex]$7 \sqrt{18} = 7 \sqrt{9 \cdot 2} = 7 \sqrt{9} \cdot \sqrt{2} = 21 \sqrt{2}$[/tex]
[tex]$\sqrt{1190700} = \sqrt{100 \cdot 11907} = \sqrt{100} \cdot \sqrt{11907} = 10 \sqrt{11907}$[/tex]
So the above are the prime factors of the given equation. Among them, the square root is not exact.
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Which describes the correct method? Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent
The option D "Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent." describes the correct method. So the option D is correct.
The substitution method is a method of solving a system of linear equations by expressing one variable in terms of the other and then substituting the expression into the other equation. This method can be used when the system of equations consists of two linear equations with two unknowns.
The elimination method is a technique used to solve systems of linear equations. It involves transforming the given system into an equivalent system of equations in which the coefficients of one of the variables are the same in each equation, and then eliminating that variable by addition or subtraction. So the option D is correct.
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Which describes the correct method?
A. Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.
B. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
C. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
D. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Problem 2 Lanny got a short term job selling computers. He is paid on
commission. In order to impress customers, he bought a few nice suits. If he has
$20 000 in sales, he will lose $140. If he has$30 000 in sales, he will make a $90
profit. Determine the:
a. rate of change and initial value
b. the amount he needs to sell to break even
c. The amount he needs to sell in order to make $1000 profit
Answer:
Step-by-step explanation:
A. the rate of change is 50
2 Let y = 3x 2 − 4x + 2. Write y in the form a(x + b) 2 + c
The required form of a(x + b)² + c to rewrite the given expression y = 3x² − 4x + 2 is given by y = 3(x - (2/3))² + 4/3.
Expression is equal to,
y = 3x² − 4x + 2
Required form to express 'y' is equal to,
a(x + b)² + c
Complete the square by adding and subtracting the square of half the coefficient of the x-term we get,
y = 3x² - 4x + 2
⇒ y = 3(x² - (4/3)x) + 2
⇒ y = 3(x² - 2(2/3)x) + 2
⇒ y = 3(x² - (4/3)x + (2/3)² - (2/3)²) + 2
⇒ y = 3(x - (2/3))² - 3(2/3)² + 2
Simplify the constant terms we have,
⇒ y = 3(x - (2/3))² - 2/3 + 2
⇒ y = 3(x - (2/3))² + 4/3
Therefore, the expression y = 3x² − 4x + 2 written in the form a(x + b)² + c is equal to y = 3(x - (2/3))² + 4/3.
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The above question is incomplete, the complete question is :
Let the expression y = 3x² − 4x + 2. Write expression y in the form
a(x + b)² + c.
Quadrilateral RSTU has vertices at T(1,11), S(9,12), T(13,5) and U(2,-2).
Show that RS is congruent to ST.
Given that RSTU is a quadrilateral with perpendicular diagonals and two adjacent, congruent sides, why isn't RSTU a rhombus?
Hence the product of the slope of RT and SU is -1, so the lines are perpendicular
RS=ST, Hence RS, and ST are congruent to each other, which is why it is a rhombus.
A particular type of rhombus is a parallelogram. In a rhombus, the opposing sides and angles are parallel and equal. The diagonals of a rhombus meet at right angles to form its shape, and it also has equal-length sides on each side. Another name for the rhombus is a diamond or rhombus. The plural of a rhombus is a rhombus or rhombuses.
Quadrilateral RSTU has vertices at T(1,11), S(9,12), T(13,5) and U(2,-2).
The slope RT is k[tex]=-\frac{1}{2}[/tex] and the slope SU is [tex]l=2[/tex]
[tex]kl=-1\\\\RS=\sqrt{8^2+1}=\sqrt65\\and ST=\sqrt(65)\\\\[/tex]
RS=ST ,
hence RS is congurent to ST
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I. The distribution is skewed left
II. The interquartile range is 6
III. The median is 22
Identify the true statement or statements.
The statement that is true about the boxplot is option (E) I, III, and IV
I. It is a left skewed distribution which has outliers.
True. The boxplot is skewed to the left, as the median line is closer to the bottom whisker than to the top whisker. Additionally, there are circles (outliers) on the left-hand side of the plot.
II. It is a symmetrical distribution which has outliers.
False. The plot is not symmetrical because the median line is not in the middle of the box.
III. The interquartile range is less than 1.
True. The box covers the range from the first quartile (Q1) to the third quartile (Q3), and the length of the box is less than 1.
IV. Approximately 75% of the observations have a GPA of less than 3.
True. The top of the box represents the 75th percentile, which is approximately 3.
Therefore, the correct option is (E) I, III, and IV
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The given question is incomplete, the complete question is:
Which statement is true about the boxplot below?
I. It is a left skewed distribution which has outliers.
II. It is a symmetrical distribution which has outliers.
III. The interquartile range is less than 1.
IV. Approximately 75% of the observations have a GPA of less than 3.
(A) I only
(B) II only
(C) II and III
(D) III and IV only
(E) I, III, and IV
A group of penguins swam 4/5 mile in 1/3 hour. How many miles did the penguins swim in one hour?
A group of penguins swam 4/5 mile in 1/3 hour, [tex]\frac{4*3}{5}=\frac{12}{5}[/tex] miles did the penguins swim in one hour.
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
We frequently employ these fundamental mathematical operations in our daily lives: +, -,, and. We employ mathematical operations for every situation when we must determine the annual budget or distribute things equitably to a lot of people.
[tex]\frac{4}{5}[/tex] miles swim in [tex]\frac{1}{3}[/tex] hour
swim in one hour = [tex]\frac{4*3}{5}=\frac{12}{5}[/tex] mile
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Overflow Pan : A metalworker makes an overflow pan by cutting equal squares with sides of length x from the
corners of a 30 cm by 20 cm piece of aluminium, as shown in the figure. The sides are then folded up and the
corners sealed.
(i) Find a polynomial function V x( ) that gives the volume of the pan.
(ii) Find the volume of the pan if the height is 6 cm. Use remainder theorem.
The polynomial function is V(x) = (30-2x)(20-2x)x and the volume of the pan is 864 cm^3.
Finding the Volume of an Overflow PanThe polynomial function
To find the volume of the pan, we first need to determine the dimensions of the base and height.
If we cut equal squares with sides of length x from the corners of a 30 cm by 20 cm piece of aluminum, then
The base of the pan will have dimensions (30-2x) cm by (20-2x) cm.The height of the pan will be x cm.Thus, the volume of the pan can be expressed as:
V(x) = (30-2x)(20-2x)x
The volume
Using the remainder theorem, we have
V(6) = (30 - 2 * 6)(20 - 2 * 6) * 6
Evaluate
V(6) = 864
Thus, when x = 6, the volume of the pan is:
V(6) = 864 cm^3.
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Solve the equation.
5(y+25)=−13
y =?
Answer:
y=-27+3/5 or 138 or 5 if need as a fraction
Step-by-step explanation:
5(y+25)-(-13)=0
add all the numbers together and all the variables
5(y+25)+13=0
multiply parentheses to get
5y+125+13=0
add all the numbers together n all the variables together to
5y+138=0
Then move all terms hat have y to the left and terms to the right
so 125 basiclly
5y=-138
y=-138/5
y=-27+3/5 aslo could be known as - 138 over 5 (fraction )
FOR 200 POINTSSSSSS
This figure consists of a rectangle and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π .
Enter your answer as a decimal in the box.
__ cm
the perimeter of the figure is approximately 48.56 cm.
What are the definitions of perimeter and its unit?The perimeter of a shape in geometry refers to its whole boundaries. The lengths of a shape's edges and sides are added to find its perimeter.
from the question:
The lengths of all the figure's sides must be added up in order to determine their perimeter.
The rectangle has two sides that are 10 cm long and two that are 8 cm long, making its perimeter:
P_rect = 2(10 cm) + 2(8 cm) = 36 cm
Since it shares a side with the rectangle, the quarter circle has a radius of 8 cm and an arc length that is one-fourth of the circle's diameter, which is:
L_circle = (1/4)(2πr) = (1/4)(2π)(8 cm) = 4π cm
Therefore, the perimeter of the figure is:
P = P_rect + L_circle = 36 cm + 4π cm ≈ 48.56 cm
The figure's perimeter, when rounded to two decimal places, is roughly 48.56 cm.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
The answer is D
Step-by-step explanation:
? → Find the pressure in kN/m2 exerted by a force of 60 kN on an area of 12 m². kN/m²
Therefore , the solution of the given problem of area comes out to be the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².
Explain area.Calculating how much room is needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capability of a cuboid is given by the total of the borders connected to each of its six rectangular edges.
Here,
The following method determines the pressure P that a force F exerts on an area A:
=> P = F/A
Inputting the numbers provided yields:
=> P = 60 kN / 12 m²
If we simplify, we get:
=> P = 5 kN/m²
As a result, the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².
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Select all the trinomials that have (3x+2) as a factor. 6x^(2)+19x+10 6x^(2)-x-2 6x^(2)+7x-3 6x^(2)-5x-6 12x^(2)-x-6
The trinomials that have (3x+2) as a factor are [tex]x^{2} 6x^2+19x+10, 6x^2-x-2\sqrt{x} \\\\[/tex] , [tex]6x^2+7x-3, 6x^2-5x-6 and 12x^2-x-6.[/tex]
A trinomial is a polynomial with three terms. Each trinomial can be written in the form ax^2+bx+c, where a, b and c are constants, and x is a variable. If a trinomial has (3x+2) as a factor, then it can be written in the form (3x+2)(ax+b). By multiplying out this expression, we can obtain the trinomial ax^2+bx+c.
To find the trinomials that have (3x+2) as a factor, we need to solve the equation ax^2+bx+c = (3x+2)(ax+b). This can be done by equating coefficients of the same powers of x. For example, equating the coefficients of x^2 gives us the equation a = 3a. Since a cannot equal both 3a and 0, we must have a = 0. Similarly, equating the coefficients of x gives us the equation b = 3b+2a, so b = -2a. Finally, equating the constants gives us the equation c = 3b+2a, so c = 2a.
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List the values for a , b , and c from the quadratic above x^2+3x-4=0
1, 3, -4
Step-by-step explanation:Second-degree functions are known as quadratics.
Quadratic Functions
Quadratic functions are second-degree. This means that the highest exponent of any term is 2. When graphed, quadratic functions form parabolas, which look like U-shape.
To find the a, b, and c values of a quadratic, the function must be set equal to zero and in standard form. Remember that standard form is when the terms are written in descending order of degree (exponent). This equation given is already set equal to zero and in standard form.
Standard Form
When in standard form, quadratics are written like ax^2+bx+c. The coefficients go in alphabetic order.
The a-value is always the coefficient of x^2The b-value is always the coefficient of xThe c-value is always the constantThis means that for the given equation: a = 1, b = 3, c = -4. These values can be used in different ways, mainly the quadratic equation.
4.02 Lesson check ! (6)
The value 8 is the common difference of the given sequence.
Determining the common difference of a sequenceA sequence is a list of objects where repeats are allowed and the order is important. It includes members, much like a set. The length of the sequence is measured by the total number of elements.
Given the sequence below
12, 20, 28, 36...
The nth term of an arithmetic sequence is given as Tn = a + (n-1)d
The common difference is the difference between the preceding and the succeeding term.
First term = 12
Second term = 20
Common difference = 20 -12 = 28 - 20
Common difference = 8
Hence the common difference of the sequence is 8
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help would be appreciated
The graph that shows the horizontal compression is graph A.
Which graph shows the transformed function?For a function f(x), we define a horizontal compression of scale factor k as :
g(x) =f(x*k)
In this case, the function f(x) is graphed at the top, and we want to identify the graph of f(4*x).
So we have a compression of scale factor k = 4.
This only changes the values in the horizontal axis, and the vertical axis remains unchanged, so option D and C can be discarded.
Now, B is a dilation and A is a compression, so the correct option is graph A.
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Use the graphs to make predictions about the relationship between the number of homeless Pit Bulls and the number of homeless Chihuahuas
Answer:
the answer to ur question is 6
Answer:
25
Step-by-step explanation:
A particular American football player threw 8486 passes and 5956 of them were caught, so his success rate is 0.702. Describe a procedure for using computer software to simulate his next pass. The outcome should be an indication of one of two results: (1) The pass is caught; (2) the pass is not caught.
Therefore , the solution of the given problem of probability comes out to be a random result will be produced with a success probability equal to the specified success rate of 0.702.
What is probability?Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .
Here,
Here is a potential Python method for modelling the subsequent pass:
Python: import the random package.
import arbitrary
0.702 is the desired performance rate:
makefile
success rate for copying is 0.702
The random.random() function can be used to produce a random integer between 0 and 1:
random.random rand num ()
Simulate the pass being caught if the random number is less than or equivalent to the success rate. If not, pretend that the throw was not caught:
python
output if rand num = success rate ("The pass is caught.")
if not: output ("The pass is not caught.")
Every time this process is executed, a random result will be produced with a success probability equal to the specified success rate of 0.702.
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56+66? 12 - 16? 80+42+ 32? 36-46? 96 -86- 42? 74-92-84?
Answer:
Step-by-step explanation:
56+ 66 = 122
12-16 = -4
80 + 42 + 32 = 154
36 - 46 = -10
96 - 86 - 42 = -32
74 - 92- 84 = -102
(In case you need the total answer of everything added up the answer is : 128 )
In a study in 1998, the following equation for predicting baby birth weight in grams (Y) given mothers age in years (X): = -1163.45 + 245.15.X. If the RMS=589.3 grams, about 95% of the babies born to a 22-year-old mothers will weigh between grams and _______grams. Hint: make sure to carry calculations to at least 4 places past the decimal. OA) (1726.5, 5262.3) OB) (4687.55, 5866.15) OC) (3051.25, 5408.49) OD) (6508.95, 7044.75) OE) (2315.8, 4673.0).
The 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).
To get started, let's put the mother's age into the given equation to determine the mean birth weight. Then, we'll use the RMS value to calculate the standard deviation.The equation for predicting baby birth weight in grams given the mother's age is: Y = -1163.45 + 245.15XWhere X is the mother's age, and Y is the baby's birth weight. We are given X=22, so let's use that to find the predicted mean birth weight:Y = -1163.45 + 245.15(22) = 4486.95 gramsThe RMS is given to be 589.3 grams. Because we're told that the distribution is approximately normal, we can use the 68-95-99.7 rule to find the 95% prediction interval. Here are the steps:Subtract the RMS from the mean to find the lower endpoint of the interval:4486.95 - (2 x 589.3) = 3308.35Add the RMS to the mean to find the upper endpoint of the interval:4486.95 + (2 x 589.3) = 5665.55Round both values to four decimal places, as instructed in the problem:3308.35 rounds to 3308.4 grams5665.55 rounds to 5665.6 gramsTherefore, about 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).
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Pls help 100 pts
If u could pls answer question a
Answer:
Step-by-step explanation:
The initial height is the beginning of the graph, or in this case, x=0. So the initial height is 1.5.
ind the complex zeros of the following polynomial function. Write f in factored form: f(x) = x^4 + 170x^2 + 169 The complex zeros of f are. (Simplify your answer. Type an exact answer, using radicals and i as needed. Use Use the complex zeros to factor f f(x) = (Type your answer in factored form. Type an exact answer, using radicals and i as
The complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169 are [-i\sqrt{2}, i\sqrt{2}, -1, 1].
To find the complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169, we can start by noting that this polynomial is a perfect square of a binomial. Specifically, we have:
f(x) = (x^2 + 13)^2
Therefore, the zeros of f(x) are the values of x that satisfy f(x) = 0. In other words, we need to solve the equation:
(x^2 + 13)^2 = 0
Taking the square root of both sides, we get:
x^2 + 13 = 0
Solving for x, we get:
x = ±i√13
However, we need to find the complex zeros of f(x), which are the roots of the equation f(x) = 0. Since f(x) = (x^2 + 13)^2, the zeros of f(x) are exactly the same as the zeros of x^2 + 13, namely ±i√13.
But this is not the end of the story. Since x^2 + 13 has only two distinct roots, namely ±i√13, each of these roots must occur with multiplicity 2 in f(x). This means that f(x) has a repeated root at each of the values ±i√13.
Finally, we note that x^2 + 13 can be factored as:
x^2 + 13 = (x + i√13)(x - i√13)
Therefore, we can write f(x) as:
f(x) = (x^2 + 13)^2 = (x + i√13)^2(x - i√13)^2
This gives us the factored form of f(x), and we can see that it has four roots, namely -i√13, i√13, -i√13, and i√13, which can be simplified to -i√2, i√2, -1, and 1.
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To have $6,000 for a child’s education in 10 years, what amount should a parent deposit in a savings account that earns 12% compounded quarterly?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6000\\ P=\textit{original amount deposited}\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]6000 = P\left(1+\frac{0.12}{4}\right)^{4\cdot 10} \implies 6000=P1.03^{40} \\\\\\ \cfrac{6000}{1.03^{40}}=P\implies 1839.34\approx P[/tex]
There are 10 observations arranged in ascending order As given below 45, 47,50,x,x+2,60,62,63. The median of this observations is 53 find the value of x also find the mean and the mode of the data
Answer:
Below in bold.
Step-by-step explanation:
The median will be the average of the 2 middle numbers
so it is:
(x + x + 2)/2 and this equal 53,
(2x + 2)/2 = 53
x + 1 = 53
x = 52.
So, the list is
45, 47, 50, 52, 54, 60, 62, 63
Mean = (45 + 47+ 50+ 52 +54+ 60+ 62+ 63)/ 8
= 54.125
There is no Mode.
3x+15+2x+20=180
solve for x