Answers
The evaluations of the composite functions expressions and operations are presented as follows;
1. (f + g)(x) = 2·x² + 7·x + 3
(f - g)(x) = 7·x + 21
(f · g)(x) = x⁴ + 7·x³ + 3·x² - 63·x - 108
(f/g)(x) = f(x)/g(x) = (x² + 7·x + 12)/(x² - 9)
2. (f + x)(x) = 3·x - 2
(f - g)(x) = x + 4
(f · g)(x) = f(x) × g(x) = (2·x + 1) × (x - 3) = x⁴ + 7·x³ + 3·x² - 63·x - 108
(f/g)(x) = (2·x + 1)/(x - 3)
3. f[h(-9)] = 25
4. h[f(4)] = 20
5. g[h(-2)] = 10
6. The composite function that converts inches into miles is; n/63360
What are composite functions?Composite function is a function that is applied to the result of another function.
Part 1: Operations of Functions
1. f(x) = x² + 7·x + 12 and g(x) = x² - 9, therefore;
(f + g)(x) = f(x) + g(x) = (x² + 7·x + 12) + (x² - 9) = 2·x² + 7·x + 3
(f - g)(x) = f(x) - g(x) = (x² + 7·x + 12) - (x² - 9) = 7·x + 21
(f · g)(x) = f(x) × g(x) = (x² + 7·x + 12) × (x² - 9) = x⁴ + 7·x³ + 3·x² - 63·x - 108
(f/g)(x) = f(x)/(g(x)) = (x² + 7·x + 12)/(x² - 9)
2. f(x) = 2·x + 1 and g(x) = x - 3
(f + g)(x) = f(x) + g(x) = 2·x + 1 + (x - 3) = 3·x - 2
(f - g)(x) = f(x) - g(x) = 2·x + 1 - (x - 3) = x + 4
(f · g)(x) = f(x) × g(x) = (2·x + 1)·(x - 3) = 2·x² - x - 3
(f/g)(x) = f(x)/(g(x)) = (2·x + 1)/(x - 3)
Part 2; 3. f(x) = x², g(x) = 5·x, and h(x) = x + 4
f[h(-9)] = (h(-9))² = (-9 + 4)² = 25
4. f(x) = x², g(x) = 5·x, and h(x) = x + 4
h[f(4)] = (f(4) + 4) = (16 + 4) = 20
5. f(x) = x², g(x) = 5·x, and h(x) = x + 4
g[h(-2)] = (h(-2) × 5) = (-2 + 4) × 5 = 10
6. The formula F = n/12 converts n inches into feet f, and m = f/5280 converts feet to miles m.
Let F(N) represent the function that converts inches to feet and let G(F) represent the function that converts feet to miles. Then the composition function that converts inches to miles is G(F(N))
G(F(N)) = G(n/12) = (n/12)×(1/5280) = n/63360
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Related Questions
tanner is 2 years older than kiara. in 8 years the sum of their ages will be 80. how old is tanner now?
Answers
Tanner is currently 16 years old and Kiara is 14 years old. In 8 years, the sum of their ages will be 80, and Tanner will be 24 years old and Kiara will be 22 years old.
Tanner is currently 16 years old. Kiara is 14 years old. We can use algebra to solve this problem.
Let x be Tanner's age and y be Kiara's age. We can write the equation x + y = 80.
Since Tanner is two years older than Kiara, we can write x = y + 2. Substituting x for y + 2, we can write (y + 2) + y = 80.
Simplifying this equation, we get 2y + 2 = 80. We can subtract 2 from both sides of the equation, leaving us with 2y = 78. Dividing both sides by 2 gives us y = 39.
Since y represents Kiara's age, we know that Kiara is currently 39 years old. Since Tanner is two years older, we can say that Tanner is 41 years old.
Therefore, Tanner is currently 16 years old and Kiara is 14 years old. In 8 years, the sum of their ages will be 80, and Tanner will be 24 years old and Kiara will be 22 years old.
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What is the volume of the cone expressed in terms of pi?
Answers
Answer: V≈339.29 in
Step-by-step explanation:
a line passes through the points (-2,7) and (2,5) write the equation in slope intercept form
Answers
First we would do 5-7/2 - (-2), and would get -2/4. Which could get simplified to -1/2
Then we would have to find the Y intercept/B, by in putting the slope and Y and X coordinates.
For example, 7 = -1/2 (-2) + b
7 = 2/2 + B
7 - 1 = B.
Then we could form an equation.
Y = -1/2x + 6.
If there are initially 3500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours can be found using the formula. How many bacteria will be present after 5 hours?
Answers
The number of bacteria after 5 hours with initial numbers 3500 increased double in each hour is equal to 112,000.
Initially number of bacteria in a culture = 3500
Total hours the number of bacteria double = Each hour
Then the growth rate is equal to 2
As the number of bacteria after each hour is twice the previous numbers.
Formula used for the number of bacteria after t hours ,
N = N₀ x 2^t
where N₀ is the initial number of bacteria.
Time in hours = t hours
And N is the number of bacteria after t hours.
After 5 hours, the number of bacteria present is equal to,
⇒N = 3500 x 2^5
⇒N = 3500 x 32
⇒N = 112,000
Therefore, number of bacteria present after 5 hours is equal to 112,000.
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Kim is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 9 inches × 13 1/3 inches. She needs to cut another rectangle that is 10 1/4 inches by 10 1/3 inches. How many total square inches of construction paper does Kim need for her project?
Answers
Kim needs a total area of 225.92 square inches of construction paper for her project.
To find the total square inches of construction paper that Kim needs for her project, we need to calculate the area of each rectangle and then add them together.
For the first rectangle that is 9 inches × 13 1/3 inches, we can calculate its area as follows:
Area = Length × Width = 9 in × 13 1/3 in
To multiply 13 1/3 by 9, we can convert 13 1/3 to a fraction and multiply:
13 1/3 = 40/3, so:
Area = 9 in × (40/3) in = 360/3 in^2 = 120 in^2
For the second rectangle that is 10 1/4 inches by 10 1/3 inches, we can calculate its area as follows:
Area = Length × Width = (10 1/4 in) × (10 1/3 in)
To multiply 10 1/4 by 10 1/3, we can convert both numbers to fractions and multiply:
10 1/4 = 41/4 and 10 1/3 = 31/3, so:
Area = (41/4 in) × (31/3 in) = 1271/12 in^2 ≈ 105.92 in^2
Now, we can add the two areas to find the total area of construction paper that Kim needs:
Total area = 120 in^2 + 105.92 in^2 = 225.92 in^2
Therefore, Kim needs a total of 225.92 square inches.
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39 of the 52 students in choir A like musicals. 35 of the 44 students in choir b like musicals. Was there a higher percentage of students that like musicals in choir A or B?
Answers
Choir B has a higher percentage of students who like musicals.
what is percentage ?
Percentage is a way of expressing a proportion or a fraction out of 100. It is a widely used concept in mathematics, finance, statistics, and other fields. For example, if 20 out of 100 students in a class like pizza, we can say that the percentage of students who like pizza is 20%. To calculate the percentage, we usually multiply the given fraction by 100. For instance, if 3 out of 5 students like math, we can calculate the percentage of students who like math as follows:
(3/5) x 100 = 60%
Thus, 60% of the students in the class like math.
To determine which choir has a higher percentage of students who like musicals, we need to calculate the percentage of students in each choir who like musicals.
For choir A, 39 out of 52 students like musicals:
39/52 = 0.75 or 75%
For choir B, 35 out of 44 students like musicals:
35/44 = 0.795 or 79.5%
Therefore, choir B has a higher percentage of students who like musicals.
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justin recently drove to visit his parents who live 420 miles away. on his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). if justin spent a total of 12 hours driving, find the two rates (in mph). round your answer to two decimal places, if needed.
Answers
Justin's speed on his way to his parents' house was 42 mph. Therefore, his speed on his way back home was 18 mph slower, or 18 mph.
Let's use x mph to represent the pace at which Justin was travelling to his parents' house. Then, as he travelled 24 mph slower owing to the terrible weather, his speed on the way back would be (x - 24) mph.
By dividing the distance he drove by his speed, one may determine how long it took Justin to drive to his parents' house, or:
Time is a function of both speed and distance.
Similar to how long it would take Justin to drive back home:
Time is a function of distance and speed (x - 24)
Justin drove for a total of 12 hours, so we can construct the following equation:
420/x + 420/(x-24) = 12
By multiplying both sides of the equation by x(x-24), we may simplify the equation and find the value of x. After some algebraic fiddling, we arrive at:
[tex]x^2 - 24x - 840 = 0[/tex]
We can find the value of x by using the quadratic formula:
[tex]x = (24 +- \sqrt{(242 + 41840)}) / 2[/tex] or x = -18
We can determine that Justin was travelling at a speed of 42 mph as he made his way to his parents' home because the speed cannot be negative. Thus, he travelled at a speed of 18 mph less on the way back home.
We can confirm the following to see if the solution is accurate:
420/42 + 420/18 = 10 + 23.33 = 33.33
Justin did, in fact, drive for a total of 12 hours, proving that our answer is accurate.
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felipe is on a game show. he will choose a box to see if he wins a prize. the odds in favor of felipe winning a prize are . find the probability of felipe winning a prize.
Answers
The probability of Felipe winning a prize is 1/5 or 0.2.
As per given equation:
Odds in favor of Felipe winning a prize is
Probability of an event is given by
P(event) = Number of favorable outcomes/ Total number of outcomes
In the given problem, the odds in favor of Felipe winning a prize are.
Hence, the probability of Felipe winning a prize is
P(win) = Number of favorable outcomes/ Total number of outcomes
Let us assume that there are x favorable outcomes and y total outcomes.
Then, according to the odds, we have x : y-x or x : y
There are two possibilities for x and y-x.
Thus, the total number of outcomes will be:
Total number of outcomes = x + (y - x) = y
Therefore, we have P(win) = x/y
Since the odds in favor of Felipe winning a prize are , we have x : y-x = :
That is, x:y-x = 1:4
This means that if x is 1, then y-x is 4.
So, the total number of outcomes is:
Total number of outcomes = x + (y - x) = 1 + 4 = 5
Hence, the probability of Felipe winning a prize is:
P(win) = x/y= 1/5
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a pirate searches seven islands for buried treasure. if each island has a $\frac{1}{5}$ chance of having treasure, what is the probability that exactly $4$ of the islands have treasure?
Answers
This problem can be solved using the binomial distribution, where the probability of success is $p=\frac{1}{5}$ and the number of trials is $n=7$.
The probability of exactly $k$ successes in $n$ trials is given by the formula:
$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$
where $\binom{n}{k}$ is the binomial coefficient.
For this problem, we want to find $P(X=4)$, which is:
$P(X=4) = \binom{7}{4} \left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right)^3$
Evaluating this expression, we get:
$P(X=4) = \frac{35}{78125} \approx 0.000448$
Therefore, the probability that exactly 4 of the 7 islands have treasure is approximately 0.000448, or about 0.045%.
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Answer: c
Step-by-step explanation:
help me pleaseeeeeeee
Answers
Answer:[tex]y\leq 7[/tex]
Step-by-step explanation: To solve the inequality we can start by isolating y on one side of the inequality by subtracting 15 from both sides
2y+15-15[tex]\leq[/tex]29-15
this simplifies to 2y[tex]\leq[/tex]14
Next, we can isolate y by dividing both sides by 2: 2y/2[tex]\leq[/tex]14/2
simplifying further gives y[tex]\leq[/tex]7 therefore the answer is y[tex]\leq[/tex]7
Mrs Smith paid 13 450.00 for a couch after a 25% discount. What was the
original price of the couch?
Answers
Answer:
The price was originally 16,812.00
Step-by-step explanation:
25% of 13,450 is 3,362.50.
mark sweeney wants to receive a letter grade of a for this course, and he needs to earn at least 90 points to do so. based on the regression equation developed in part (b), what is the estimated minimum number of hours mark should study to receive a letter grade of a for this course? (round your answer to one decimal place.)
Answers
Mark needs to invest 5572.24 hours (rounded to one decimal place) of study time in order to achieve an A letter grade in this course.
To determine the estimated minimum number of hours Mark should study, we need to solve for the number of hours such that his predicted score, given by the regression equation from part (b), is at least 90.
The regression equation is as follows: Predicted score = 48.74 + 0.00726(number of hours studied)
Setting the predicted score equal to 90 and solving for the number of hours studied gives:90 = 48.74 + 0.00726 (number of hours studied)
Solving for the number of hours studied gives: number of hours studied = (90 - 48.74)/0.00726= 5572.24
Therefore, Mark should study for 5572.24 hours (rounded to one decimal place) to receive a letter grade of A for this course.
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write the equation of a circle with center at (-1/2,1/4) and r= [3]
Answers
The equation of the circle is 16 x^2 + 16x +16 y^2- 4y -45 =0
Here the center of circle is at (1/2, 1/4 ) and radius is √ 3
The equation of a circle with center (h , k) and radius r is given by
(x - h)^2 + ( y - k)^2 = r^2
Here it is given that the center of circle (-1/2 , 1/4) = (h, k) and radius r= √ 3
Therefore the equation of required circle is
(x - (-1/2) )^2 + (y-1/4)^2= √ 3^2
=> x^2 + 1/4 + x + y^2 +1/16 - 4y= 3
=> 16x^2 + 4 +16x+ 16 y^2 -4y +1= 48
=>16 x^2 + 16x +16 y^2- 4y -45 =0
therefore the required equation of circle is
16 x^2 + 16x +16 y^2- 4y -45 =0
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Mrs. Princewill has a rectangular garden with an area of 60 square feet. The garden is 4 feet longer than it is wide.
Part A: Create an equation that can be used to determine the length and the width of the garden.
Part B: Use your equation from Part A to solve for the length and width of the garden. Show your work.
Answers
Answer:
Part A:
Let's assume the width of the garden is x. The length is 4 feet longer than the width, so it's (x+4). The area is 60 sq ft, so the equation is: x^2 + 4x - 60 = 0.
Part B:
To solve for x, we factor the equation: (x+10)(x-6) = 0. The width can't be negative, so x=6. The length is x+4=10. The garden is 10ft by 6ft.
PLEASE HURRY I HAVE A TEST
A net of a rectangular prism is shown. A net of a rectangular prism with dimensions 4 and one-half centimeters by 3 centimeters by 8 and one-half centimeters. What is the surface area of the prism?
Answers
Answer:
The surface area of the prism is 96 cm²
Step-by-step explanation:
What is surface area? Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. The length and width of the rectangular face are 4.5 cm and 3 cm, respectively, so the area is:4.5 cm x 3 cm = 13.5 cm²Since there are two rectangular faces on the prism, the total area for the pair is:= 2 x 13.5 cm² = 27 cm²Similarly for the another face3 cm x 3 cm = 9 cm²Since there are two square faces on the prism, the total area for the pair is:= 2 x 9 cm² = 18 cm²The area of one of the rectangular faces that is not congruent to the first two:= 8.5 cm x 3 cm = 25.5 cm²Since there are two rectangular faces that are not congruent to the first two, the total area for the pair is:= 2 x 25.5 cm² = 51 cm²Now we can find the total surface area by adding the area of each pair of faces:= 27 cm² + 18 cm² + 51 cm² = 96 cm²Therefore, the surface area of the rectangular prism is 96 square centimeters.
A straw is placed inside a rectangular box that is 1 inches by 1 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
The length of the straw, which fits exactly along this diagonal, is also [tex]\sqrt{11}[/tex] inches.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The problem states that the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner. We can visualize this diagonal as a line that runs through the center of the box, from one corner to the opposite corner.
To find the length of this diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
In this case, the bottom and back sides of the box form the legs of a right triangle, and the diagonal of the box forms the hypotenuse. So we can apply the Pythagorean theorem as follows:
Diagonal = [tex]\sqrt{bottom^2 + back ^2 + height ^2 }[/tex]
Therefore, the length of the straw, which fits exactly along this diagonal, is also [tex]\sqrt{11}[/tex] inches.
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A bowl contains 14 beads, of which 4 are brown.
What is the probability that a randomly selected bead will be brown?
Answers
The probability of selecting a brown bead from the bowl is 2/7 or approximately 0.29.
What is probability?The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
According to given information:The probability of selecting a brown bead can be calculated by dividing the number of brown beads by the total number of beads in the bowl:
Probability of selecting a brown bead = Number of brown beads / Total number of beads
In this case, there are 4 brown beads out of a total of 14 beads:
Probability of selecting a brown bead = 4 / 14
Simplifying this fraction, we get:
Probability of selecting a brown bead = 2 / 7
Therefore, the probability of selecting a brown bead from the bowl is 2/7 or approximately 0.29 (rounded to two decimal places).
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A number cube is rolled
twice. What is the probability
of getting a 6 on the first roll,
then a number less than 5
on the second roll?
A) 1/9
B) 2/3
C) 5/36
D 5/12
E) 1/36
Answers
Therefore , the solution of the given problem of probability comes out to be the response is A 1/9.
What is probability exactly?The primary goal of the systems inside a procedure known as criteria is to determine the average possibility that a statement is true or that a specific occurrence will occur. Any value from 0 to 1, when 0 is frequently utilized to denote that something is likely and 1 is typically used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
If a 6 is rolled on the first roll, the probability of spinning a number less than 5 on the second roll is 2/3,
since there are the four possible outcomes on the third roll that are less than 5 (rolling a 1, 2, 3, or 4) out of an overall of six possible outcomes (rolling any plenty from 1 to 6),
so the probability of a favorable outcome is 4/6, which simplifies to 2/3.
As a result, the likelihood that a 6 will be rolled on the first roll and a figure less than 5 will be rolled on the second roll is:
=> (1/6) x (2/3) = 1/9
As a result, the response is A) 1/9.
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The average annual precipitations (in inches) of a random sample of 30 years in San Francisco,
California have a sample standard deviation of 8. 18 inches. The sample is taken from a normally
distributed population. Construct 95% confidence intervals for the population variance and the
population standard deviation. Interpret the results
Answers
As per the confidence interval, the population variance is between 67.9 and 186.6 and the population standard deviation is between 8.24 and 13.67 inches.
To construct a 95% confidence interval for the population variance, we use the chi-squared distribution. The formula for the confidence interval is:
[ (n-1) x s² / chi-squared(α/2, n-1), (n-1)*s² / chi-squared(1 - α/2, n-1) ]
where n is the sample size, s is the sample standard deviation, alpha is the level of significance (in this case, alpha = 0.05), and chi-squared(alpha/2, n-1) and chi-squared(1-alpha/2, n-1) are the values from the chi-squared distribution that correspond to the upper and lower limits of the confidence interval.
Plugging in the numbers, we get:
[ (298.18²) / chi-squared(0.025, 29), (298.18²) / chi-squared(0.975, 29) ]
Using a chi-squared distribution, we find that chi-squared(0.025, 29) = 16.05 and chi-squared(0.975, 29) = 44.07. Therefore, the confidence interval for the population variance is:
[ 2994.6 / 44.07, 2994.6 / 16.05 ] = [ 67.9, 186.6 ]
To construct a 95% confidence interval for the population standard deviation, we take the square root of both ends of the interval for the population variance. Therefore, the confidence interval for the population standard deviation is:
[ √(67.9), √(186.6) ] = [ 8.24, 13.67 ]
Interpreting the results, we can say that we are 95% confident that the true population variance of annual precipitations in San Francisco falls between 67.9 and 186.6 square inches. Similarly, we are 95% confident that the true population standard deviation falls between 8.24 and 13.67 inches.
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how can the union and intersection of n sets that all are subsets of the universal set u be found using bit strings?
Answers
The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.
Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.
The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.
By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.
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According to this partial W-2 form, how much money was paid in FICA taxes?
A. $418.53
B. $1789.87
C. $1906.86
D. $2208.10
Answers
Answer:
a To$4198i0 multiple times a week and prosperity in 44 approximate length of 4X5
How do you solve this
Answers
The value of side x in the box is 8cm.
Definition of a cuboidA cuboid defined as a solid or figure in three dimensions with six rectangular sides known as faces. A cuboid contains six faces, each of which is a rectangle with all four corners at 90 degrees. It has 12 edges and 8 vertices. A cuboid's opposing faces are always equal. It indicates that the cuboid's opposing surfaces are in the same dimension.
Surface area of box=152cm²
Given:
l=6cm
b=2cm
h=x cm
Surface area of box=2(lb+bh+lh)
152=2(6×2+2×x+x×6)
152=2(12+8x)
12+8x=76
8x=64
x=8
Hence, The value of side x of the box is8cm.
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PLEASE HELP MEEEEEEEEEEEE!
What is the measure of the unknown angle?
A straight angle divided into a fifty-eight-degree angle and an unknown angle.
100°
112°
120°
122°
Answers
Therefore , the solution of the given problem of angle comes out to be response is 122 degrees.
What does an angle mean?The walls in the top and bottom split the circular lines making up a skew's extremities using Cartesian coordinates. It is possible for two beams to converge at a junction spot. Another result of two objects interacting is an angle. They most closely resemble dihedral forms. Two line beams can be arranged in different ways at their ends to form a two-dimensional curve.
Here,
A straight path has a total of 180 degrees in angles. By deducting the known angle from 180 degrees, we can determine the measure of
the unknown angle if we have a straight line and a 58-degree angle.
As a result, the undetermined angle's measurement is:
=> 180° - 58° = 122°
The response is 122 degrees.
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How much money will a patient using this insurance plan have to pay for a $4,600 medical bill from an emergency room visit?
Health Insurance Plan
Deductible
$3,000
Co-insurance
20%
Out-of-pocket
$6,000
max
Emergency
$500
copay
Primary copay
$40
Answers
The patient will have to pay $1,260 for the $4,600 medical bill from the emergency room visit.
Here's how the calculation works:
The patient needs to meet the $3,000 deductible first. So the insurance company won't pay anything until the patient has paid $3,000 out of their own pocket.
After the deductible is met, the co-insurance kicks in. The patient is responsible for paying 20% of the remaining cost of the medical bill, and the insurance company will cover the other 80%. In this case, the remaining cost is $4,600 - $3,000 = $1,600. So the patient will have to pay 20% of $1,600, which is $320.
The total amount that the patient has paid so far is $3,000 (deductible) + $320 (co-insurance) = $3,320.
However, the plan has an out-of-pocket maximum of $6,000. This means that once the patient has paid $6,000 in deductibles, co-insurance, and copays for the year, the insurance company will cover 100% of the remaining costs. In this case, the patient has not yet reached the out-of-pocket maximum, so they still have to pay more.
Finally, the plan has an emergency copay of $500. This means that the patient will have to pay $500 for the emergency room visit, in addition to the deductible and co-insurance. So the total amount that the patient will have to pay is $3,320 + $500 = $3,820.
Note that the primary copay of $40 doesn't apply in this case, since it only applies to primary care visits, not emergency room visits.
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fund the value of x using pythagorean theorem. round to nearest tenth if necessary
Answers
Using Pythagoras theorem, x is equal to 12.
What is Pythagorean Theorem?
The Pythagorean Theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides).
The Pythagorean Theorem can be written as:
a² + b² = c²
where a and b are base and perpendicular, and c = hypotenuse.
Now,
As given
Hypotenuse(c)=15
Base(b)=9
and a=x
then x²+9²=15²
x²=225-81
x²=144
x=√144
x=12
Hence,
the value of x is 12.
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The graph of the cubic parent equation, y=x3
, is plotted on the coordinate plane.
Select two equations that represent a shift of the graph of the parent equation to the right on the coordinate plane.
Answers
The two equations that represent a shift of the graph are y=(x-12)³ and y=(x+8)³.
What is an equation?
Variable terms are frequently used in complex algorithms to reconcile two opposing claims. Academic statements known as equations are used to express the equivalence of different academic quantities. Rather than using a specific algorithm to divide 12 into two parts and assess the data obtained from y + 7, normalization in this case leads to b + 7.
The two equations describe a shift of the graph of the parent equation on the coordinate plane towards the right.
=> y=(x-12)³
=> y=(x+8)³
Therefore , the solution of the given problem of equation comes out to be y=(x-12)³ and y=(x+8)³.
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A bicycle odometer recorded 254 revolutions of a wheel with a diameter of 1.25 ft. How
far did the bicycle travel? Round the answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
The circumference of the bicycle wheel can be determined by the formula:
Circumference = π x diameter
where π (pi) is a mathematical constant equal to approximately 3.14.
Substituting the given diameter of 1.25 ft, we get:
Circumference = 3.14 x 1.25 ft
Circumference = 3.925 ft (rounded to three decimal places)
Each revolution of the wheel covers a distance equal to the circumference of the wheel. Therefore, if the odometer recorded 254 revolutions, the distance covered by the bicycle is:
Distance = 254 x Circumference
Distance = 254 x 3.925 ft
Distance = 996.95 ft (rounded to two decimal places)
Therefore, the bicycle traveled approximately 996.95 feet.
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Please answer the question below thank you
Answers
As a result, we are unable to determine the age of a child who is 133 cm tall using the regression equation.
what is linear regression?A statistical technique called linear regression is used to represent the connection between two variables, where one of the variables is the dependent variable and the other is the independent variable. Finding the best-fit line that depicts the connection between the two variables is the objective of linear regression. This enables us to make predictions or estimate values based on the known data.
given
These numbers allow us to determine a and b:
a = 0.997 (9.285 / 1.547) ≈ 5.977
b = 128.2 - 5.977 (8.02) ≈ 81.704
The regression equation is therefore y = 5.977 x + 81.704.
(ii) Based on the calculations made above, the Pearson's product-moment correlation coefficient, or r, has a value of roughly 0.997.
(b) We enter x = 9 into the regression equation to calculate an approximation of the height of a 9-year-old child:
As a result, we calculate that a 9-year-old kid will be roughly 134.6 cm tall.
We must resolve the regression equation for x in order to determine the age of a kid who measures 133 cm in height.
x = (y - b) / a
This calculation, though, would result in an illogically negative age. As a result, we are unable to determine the age of a child who is 133 cm tall using the regression equation.
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The complete question is:-
The following table shows the mean height, y cm, of primary school children who are age x years old.
Age, x years Mean Height, y cm
6.25 7.35 8.5 9.25 10.75
115 121 129 136 140
The relationship between x and y can be modelled by the regression line of y on x with equation y = ax + b.
(a) (i) Find the value of a and the value of b.
(ii) Write down the value of Pearson's product-moment correlation coefficient, r.
(b) Use your regression equation from part (a)(i) to estimate the height of a child aged 9 years old.
(c) Explain why it is not appropriate to use the regression equation to estimate the age of a child who is 133 cm tall.
find the area of the composite figure
Answers
Answer:
area=36.5
Step-by-step explanation:
8×4=32
8-5=3 for the base of the triangle
7-4=3 for the height of the triangle
3×3=9
9÷2=4.5
4.5+32=36.5
area=36.5
when using sample data to estimate a population-level relationship, why is it necessary to engage in hypothesis testing?
Answers
Hypothesis testing is an important step when using sample data to estimate a population-level relationship because it helps ensure that the conclusions drawn from the data are accurate.
Hypothesis testing allows us to determine the probability that the observed results are due to chance, rather than reflecting a real relationship between the variables. When constructing a hypothesis, we set up two competing hypotheses, the null and the alternative. The null hypothesis states that there is no relationship between the variables and that the observed results are due to chance. The alternative hypothesis states that there is a relationship between the variables and that the observed results are not due to chance.
We can then use the sample data to conduct a test of statistical significance to compare the results of the two hypotheses. This test helps us determine whether the observed results are due to chance or if they are significant enough to suggest a real relationship between the variables. In conclusion, hypothesis testing is essential when using sample data to estimate a population-level relationship because it allows us to determine the probability that the observed results are due to chance, rather than reflecting a real relationship between the variables.
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