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A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in
your answer.
5ft
9ft
SLS
6ft
6ft
0
8 08
ft
X
ft²
Ś
ft ³
E
Answers
Thus, the area of the shaded region which is found by subtracting the right triangle's area from the rectangle is 30 sq. in.
Explain about the right triangle:Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees. The internal 90° angle of right triangles is denoted by a little square in the vertex.
Given data:
Dimensions of rectangle - 10 in x 5 inbase of right triangle b = 8 inShaded area = area of rectangle - area of right triangle
Shaded area = length * width - 1/2*base*height
Shaded area = 10*5 - 1/2*8*5
Shaded area = 50 - 20
Shaded area = 30 sq. in.
Thus, the area of the shaded region which is found by subtracting the right triangle's area from the rectangle is 30 sq. in.
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complete question-
A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region.
Dimensions of rectangle - 10 in x 5 in
base of right triangle b = 8 in
Related Questions
In trapezoid ABCD, O is the point of intersection from the diagonals. The area of AOD is 15 ft^2. The altitudes from B and O to the longer base are in a 5:3 ratio. Find the area of ABD and the area of MOC if M is the midpoint of the leg CG
Answers
If M is the midpoint of the leg CG, then the
a) Area of ABD = 18.75 ft^2
b) Area of MOC = 15 ft^2
To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.
First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write
AB/CD = AD/CO
Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:
AB/CD = BC/CO
We also know that the area of AOD is 15 ft^2
Area of ABD/ Area of COD = AB/CD
We can substitute the ratio AB/CD from the similarity relation above to get
Area of ABD/ Area of COD = BC/CO
Since the bases of the trapezoids are parallel
Area of ABD/ Area of COD = BD/CO
Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write
Area of ABD/ Area of COD = 5/3
Area of ABD = 5/8 × Area of COD
We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore
Area of ABD = 5/8 × 30 = 18.75 ft^2
Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.
Let x be the length of OC, and let y be the length of OG. Then we have
Area of MOC/ Area of MOG = x/y
Also, since M is the midpoint of CG, we have
x = 2y
Substituting this into the first equation, we get
Area of MOC/ Area of MOG = 2
We know that the area of MOG is half the area of AOD, so
Area of MOG = 15/2 ft^2
Therefore, we have
Area of MOC = 2 × Area of MOG = 15 ft^2
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if a contingency table has nine rows and columns, how many degrees of freedom are there for the test for independence?
Answers
There are 64 degrees of freedom for the test for independence in this contingency table.
To find the degrees of freedom for a test for independence in a contingency table, you can use the following formula:
Degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
In your case, the contingency table has nine rows and nine columns. Using the formula:
df = (9 - 1) * (9 - 1)
df = 8 * 8
df = 64.
In a contingency table, the degrees of freedom (df) for the test of independence are calculated as:
df = (number of rows - 1) x (number of columns - 1)
In this case, the contingency table has nine rows and nine columns, so the degrees of freedom are:
df = (9-1) x (9-1) = 64
This means that there are 64 degrees of freedom for the test of independence.
Degrees of freedom are important because they determine the critical values for the test statistic, which in turn affects the decision to reject or fail to reject the null hypothesis.
In general, as the degrees of freedom increase, the critical values decrease, making it easier to reject the null hypothesis.
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There are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.
To determine the degrees of freedom for the test for independence in a contingency table with nine rows and columns, we use the formula df = (r-1)(c-1), where r is the number of rows and c is the number of columns.
Substituting in the values, we get:df = (9-1)(9-1)df = 8 x 8df = 64A contingency table is a table that shows the frequency distribution of two or more categorical variables.
A test for independence is a statistical test that checks whether the variables are related or not.
Therefore, there are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.
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the box plots below show the heights (in centimeters) of the players on the university of maryland women's basketball and field hockey teams. 2 horizontal boxplots titled basketball team and field hockey team are graphed on the same horizontal axis, labeled height, in centimeters. the boxplot titled basketball team has a left whisker which extends from 165 to 173. the box extends from 173 to 191 and is divided into 2 parts by a vertical line segment at 188. the right whisker extends from 191 to 203. the boxplot titled field hockey team has a left whisker which extends from 157 to 160. the box extends from 160 to 168 and is divided into 2 parts by a vertical line segment at 163. the right whisker extends from 168 to 178. all values estimated. which pieces of information can be gathered from these box plots? choose all answers that apply: choose all answers that apply: (choice a) the basketball players are taller on average. a the basketball players are taller on average. (choice b) the heights of the basketball players vary noticeably more than those of the field hockey team. b the heights of the basketball players vary noticeably more than those of the field hockey team. (choice c) none of the above c none of the above
Answers
Pieces of information can be gathered from these box plots are:
(a) On average, the basketball players are taller.
(b) The heights of the basketball players vary noticeably, more than field hockey team.
What is indetail explaination of the both answer?From the given information, we can gather the following pieces of information:
(a) The basketball players are taller on average. This can be inferred from the fact that the median (the vertical line segment within the box) of the basketball team's heights (188 cm) is higher than the median of the field hockey team's heights (163 cm).
(b) The heights of the basketball players vary noticeably more than those of the field hockey team.
This can be inferred from the interquartile range (IQR) of the basketball team's heights, which is from 173 cm to 191 cm (a difference of 18 cm), and the IQR of the field hockey team's heights, which is from 160 cm to 168 cm (a difference of 8 cm).
Additionally, the whiskers of the basketball team's boxplot are longer than those of the field hockey team's boxplot, indicating that there is greater variability in the heights of the basketball players.
Therefore, the correct answers are (a) the basketball players are taller on average and (b) the heights of the basketball players vary noticeably more than those of the field hockey team.
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which type of proposition claims the most knowledge due to the fact that both of its terms are distributed
Answers
In both cases, the subject term (S) and the predicate term (P) are distributed, which means that the proposition makes a claim about the entire class of S and the entire class of P.
Traditional categorical logic, a proposition with both of its terms (subject and predicate) distributed is called a universal proposition.
Stronger claim than a particular proposition.
A universal proposition is a statement that applies to all members of a category or class.
Asserts that the subject term is either entirely included or entirely excluded from the predicate term.
There are two types of universal propositions:
Universal affirmative proposition (A): All S are P.
Universal negative proposition (E): No S are P.
"All mammals are warm-blooded" is a universal affirmative proposition (A) because it claims that the subject term (mammals) is entirely included in the predicate term (warm-blooded).
It distributes both terms and claims the most knowledge.
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what equation represent
Answers
Answer: I'll have to say it's C or D but I think it's D
Hope it helped :D
The point-slope form ofthe equation of the line that passes through ( 4, -3) and (12, 1) is y - 1 = 4(x - 12). What
the standard form of the equation for this line?
O x- 4y = 8
О x-4y = 2
О 4x-y=8
• 4x-y = 2
Answers
Answer:
4x - y = 2,
Step-by-step explanation:
The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, we are given that the line passes through the points (4, -3) and (12, 1). The slope of the line is then m = (1 - (-3)) / (12 - 4) = 1/4.
Substituting the slope and the point (4, -3) into the point-slope form of the equation, we get y - (-3) = 1/4(x - 4). Simplifying, we get y + 3 = 1/4x - 1.
To convert the equation to standard form, we multiply both sides of the equation by 4. This gives 4y + 12 = x - 4. Simplifying, we get 4x - y = 8.
Therefore, the standard form of the equation of the line is 4x - y = 8.
Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 20 inches long. What is the side length of each piece?
1. 10√2
2. 20√2
3. 10√3
4. 20√3
Answers
Answer:
The correct answer is:
10√2
Explanation:
In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.
In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.
Let's denote the side length of each square as "s" inches.
According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
In this case, the hypotenuse is 20 inches, so we have:
20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)
400 = 2s^2
Dividing both sides by 2, we get:
200 = s^2
Taking the square root of both sides, we get:
s = √200
Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:
√200 = √(100 x 2) = 10√2
So, the side length of each quilt piece is 10√
The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.
This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).
[tex]h = \sqrt{p^2 + b^2}[/tex]
Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.
20 = √2p² (since p and b are equal, b can be taken as p)
On squaring both sides,
400 = 2p²
p² = 400/2
p² = 200
p = √200
p = 10√2 = b
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A class has 8 students who are to be assigned seating randomly. What is the
probability that the students will be arranged in order from shortest to tallest? Show
your work
Answers
The probability that the students will be arranged in order from shortest to tallest is 1/(8!) or 1/40320.
What is student?Student is an individual who is enrolled in an educational institution such as a university, college, or a trade school. A student typically takes courses in order to further their knowledge and skills, to prepare for further education or training, or to receive credentials necessary to pursue a job or career. Students can include both full-time and part-time learners. Depending on the institution, a student may also be referred to as a pupil, student-athlete, or scholar. Students can also take part in a variety of student-led activities and organizations, both on-campus and off-campus.
This is because there are 8! (8 factorial) ways in which the students can be arranged in order from shortest to tallest.
Therefore, the probability of any one arrangement is 1/8!
Thus, the probability of the students being arranged in order from shortest to tallest is 1/8! or 1/40320.
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A surveyor interviews a random sample of 85,349 adults in Florida and finds that 72% state that they have visited a doctor within the past year. Records from the state board of health indicate that of the 21 million Florida residents, 12 million visit a doctor annually. Identify the population, parameter, sample, and statistic. Population: 57%; parameter: 21 million; sample: 72%; statistic: 85,249
Population: 21 million; parameter: 57%; sample: 85,249; statistic: 72%
Population: 21 million; parameter: 72%; sample: 85,249; statistic: 57%
Population: 85,249; parameter: 72%; sample: 21 million; statistic: 57%
Answers
Answer:
Population: 21 million; parameter: 57%; sample: 85,349; statistic: 72%.
Explanation:
The population is the entire group being studied, which in this case is all the residents of Florida, with a total population of 21 million.
The parameter is a numerical summary of the population, which in this case is the proportion of residents who visit a doctor annually and is stated as 57% in the problem.
The sample is a subset of the population that is selected for study, which in this case is the 85,349 adults surveyed by the surveyor.
The statistic is a numerical summary of the sample, which in this case is the proportion of adults in the sample who stated that they have visited a doctor within the past year and is stated as 72% in the problem.
1.12x - 2.24y= 4.96 -3.56- 2.48y= -7.32
Answers
An item is regularly priced at 50 It is now priced at a discount of 70% off the regular price. What is the price now
Answers
Answer: $15
Step-by-step explanation:
If you have a 70% coupon for a $50 item, that means you are only paying 30% of the normal price.
0.3 x 50 = 15
The item will cost $15
Eight identical lights are connected in series across a 110-V line. What is the voltage across each bulb? If the current is 0.56A , what is the resistance of each bulb? If the current is 0.56A , what is the power dissipated in each?
Answers
The resistance of each bulb that is connected in series with a 110 V line is 24.55 Ω with a 13.75 V Voltage difference across each bulb. The power dissipated in each bulb is 7.7 W, if 0.56 A current flows through them.
The voltage across 8 identical bulbs is 110 V
Since they are connected in a series and identical, the Voltage difference across each bulb is [tex]\frac{110}{8}[/tex] V which is 13.75 V
According to the question,
The current flowing through the bulb = 0.56 A
So according to Ohm's Law,
V = IR
13.75 = 0.56 * R
R = 24.55 Ω
The power dissipated in each bulb can be calculated as
P = VI
P = 13.75 * 0.56 = 7.7 W
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In summary, the voltage across each bulb is 13.75V, the resistance of each bulb is 24.55Ω, and the power dissipated in each bulb is 7.7W.
When eight identical lights are connected in series across a 110-V line, the voltage across each bulb will be 110/8 = 13.75 V.
To find the resistance of each bulb, we can use Ohm's law, which states that resistance is equal to voltage divided by current (R = V/I). Therefore, the resistance of each bulb is 13.75/0.56 = 24.55 ohms.
To find the power dissipated in each bulb, we can use the formula P = VI, where P is power, V is voltage, and I is current. Therefore, the power dissipated in each bulb is 13.75 x 0.56 = 7.7 watts.
To find the voltage across each bulb, divide the total voltage by the number of bulbs:
Voltage across each bulb = Total Voltage / Number of Bulbs = 110V / 8 = 13.75V per bulb
Next, use Ohm's Law to find the resistance of each bulb:
Resistance (R) = Voltage (V) / Current (I) = 13.75V / 0.56A = 24.55Ω per bulb
Finally, find the power dissipated in each bulb using the formula:
Power (P) = Voltage (V) x Current (I) = 13.75V x 0.56A = 7.7W per bulb
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consider a dataset of towers in every state which is normally distributed. consider a sample of 40 towers. the sample data has a mean of 68 with a standard deviation of 15. how many degrees of freedom we use to find the t-critical statistic value?
Answers
39 degrees of freedom will be used to find the t-critical statistic value.
We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.
The degrees of freedom (df) for a t-distribution are calculated as given below:
df = n - 1
where n is the sample size of the problem.
In this case, the sample size is 40, so the degrees of freedom would be:
df = 40 - 1 = 39
Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.
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Kaylee borrows 700 dollars from her dad to buy a new phone. She has to pay him back in 2 years with a 2% simple intrest rate. How much interest will she have to pay?
Answers
The interest she will have to pay is $28.
Jordan is looking for a new place to live. She saw an ad in the paper and went to
the apartment building to look at the available unit. There, she met Steve, the
person who manages the property. Steve's jobs include collecting rent, making
small repairs, and screening the people who answers the ads. The rent checks
are to be made to Dave, the owner of the building. Jordan loves the apartment
and is approved to sign the lease and move in.
In this scenario, Steve is the:
O Real estate agent
O Tenant
O Landlord
O Property manager
Answers
Based on the given scenario, Steve who manages the property is a real estate agent.
The correct answer choice is option A
Who is a real estate agent?A real estate agent is a person who serves as n intermediary between tenant and landlord, buyers and sellers of properties. They collect rent, make little repairs and screen interested people. The real estate agent receives their reward based on commission, that is, a particular percentage of the property.
Therefore, Jordan is the tenant, Dave is the landlord and Steve is the real estate agent.
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The prism below is made of cubes which measure of a centimeter on one side.
Which of the following represents the volume of the prism?
There are multiple answers.
3/2 cubic cm
1/216 cubic cm x 24
4/3 cubic cm
1/18 cubic cm x 24
1/9 cubic cm
(4 x 1/6cm) + (2 x 1/6cm) + (3 x 1/6cm)
(4 x 1/6cm) X (2 x 1/6cm) X (3 x 1/6cm)
NO LINKS NO FILES
Answers
The prism has an 8/27 cubic centimetre volume.
What is the volume of a cube?The following formula determines a cube's volume:
V = s³
where V is the volume of the cube and s is the length of one of its sides.
In other words, to find the volume of a cube, you simply need to raise the length of one of its sides to the third power (cube it).
The volume of a cube = s³
Given that the prism is composed of cubes with a one-third-centimeter side measurement.
Volume of a cube = (1/3)³ = 1/27
There are 8 cubes in the prism.
Therefore, the volume of the prism is;
=8(1/27)
= 8/27 cubic centimeter.
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The complete question is:
The prism below is made of cubes which measure of a centimeter on one side. What is the volume?
Note: Figure is not drawn to scale.
The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?
Image is attached below.
you have a six-sided die t hat youroll once and observe the number of dotsfacing up,vards. \t\fhat is the sample space?\i\fhat is the probability of each sample outcome? \i\fhat is the probability of e, theevent that t he roll is even?
Answers
The sample space is {1, 2, 3, 4, 5, 6}.
The probability of each sample outcome is 1/6.
The probability of the event that the roll is even is 1/2.
Algunos números irracionales no tienen inverso aditivo
Answers
The statement " Some irrational numbers do not have an additive inverse" is false because every real number, whether rational or irrational, has an additive inverse.
Every real number, whether rational or irrational, has an additive inverse. The additive inverse of a real number x is the number that, when added to x, gives zero as the result. For any real number x, its additive inverse is -x.
This is a fundamental property of the real numbers and is true regardless of whether a number is rational or irrational. Therefore, any irrational number, such as the square root of 2 or pi, also has an additive inverse. For example, the additive inverse of the irrational number √2 is -√2, since √2 + (-√2) = 0.
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which of the following is not one of the assumptions that should be met before conducting an independent groups t-test? the dependent variable should be measured on at least an interval level scale. the dependent variable scores should be normally distributed in their parent populations. the samples should have the same number of participants.the samples should be randomly selected.
Answers
The assumption that should not be met before conducting an independent groups t-test is that the samples should have the same number of participants.
How to find the assumption that should not be met before conducting an independent groups t-test?An independent groups t-test is a statistical test used to compare the means of two independent groups of data. Before conducting this test, there are several assumptions that should be met to ensure the validity of the results. The first assumption is that the dependent variable should be measured on at least an interval level scale.
This means that the values of the dependent variable should be meaningful and can be compared using mathematical operations such as addition and subtraction. The second assumption is that the dependent variable scores should be normally distributed in their parent populations. This means that the distribution of scores should resemble a bell-shaped curve, with most scores clustering around the mean and fewer scores at the tails.
The third assumption is that the samples should be randomly selected to ensure that the sample is representative of the population from which it was drawn. The fourth assumption is that the samples should have approximately equal variances to ensure that the test is not biased towards one sample over the other. If any of these assumptions are violated, the results of the t-test may not be reliable.
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See image. If you can show work please do so otherwise thank u in advanced
Answers
From the figures, AB is a tangent to the C because they make a right angles (90⁰)
What is a tangent to a circle?Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.
We shall be determining the angle at C to see if it gives 90⁰
Using trigonometrical ratios of tangent
TanB = Opposite/Adjacent
Tan B. = 4.8/7.2
Tan B = 0.6667
B = Tan⁻¹0.6667
<B = 33.69⁰
Also in the same manner,
TanS = opp/Adj
Tan S = 7.2/4.8
Tan S = 1.5
S = Tan⁺¹1.5
< S = 56.31⁰
Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰
Therefore AB makes tangent at C
20.
Tan C = Opp/Adj
Tan C = 15/11.2
Tan C = 1.3393
C = Tan⁺¹1.3393
< C = 53.25
Also, Tan B = 11.2/15
Tan B = 0.7467
B = 36.75
<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰
Therefore AB makes a tangent at C
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(Repost because urgency)
Not sure how to go about tackling this question?
Should I try to get [tex]y=\frac{x(k+1)}{k-1}[/tex] into the form of the ratio by rationalizing first then simplify?
Answers
Answer:
y = [tex]\frac{x(k+1)}{k-1}[/tex]
Step-by-step explanation:
First, recall that in a proportion (a set of equivalent ratios), the product of means is equal to the product of extremes. For example,
if [tex]\frac{a}{b} = \frac{c}{d}[/tex] (or a:b = c:d) the product of means (b and c) is equal to the product of extremes (a and d), and we have ad = cb.
Using this knowledge, in the proportion (y+x):(y-x) = k:1, let us find the product of means and extremes and set them equal, like so:
(y+x):(y-x) = k:1 =
k(y-x) = y+x =
ky - kx = y+x
To solve for y, move all terms including y to one side, like so:
ky - kx = y+x =
ky - y = kx + x
Now, factor out y.
ky - y = kx + x =
y(k - 1) = kx + x
Then, factor out the common term x.
y(k - 1) = kx + x =
y(k - 1) = k(x + 1)
Now, finish isolating the variable by dividing by (k-1), and we have:
y = [tex]\frac{x(k+1)}{(k-1)}[/tex]
What ordered pair is represented by the function g(4) = 22?
Answers
Ordered pair is represented by the function g(4) = 22 is (4,22)
Define ordered pairAn ordered pair is a pair of mathematical elements written in a specific order, typically represented by the notation (a, b). The first element in the pair is called the x-coordinate, while the second element is called the y-coordinate. The order of the elements is important, so (a, b) is not the same as (b, a) unless a = b.
Ordered pairs are commonly used in mathematics to represent points in the Cartesian plane, where the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin. They can also be used to represent solutions to equations, inputs and outputs of functions, and many other mathematical concepts.
Given Function
g(4)=22
For the value of x=4
The output of function is y=22
So, the ordered pair is (4,22).
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PLS HELP SOLVE W STEPS!!!! THANK YOU
Answers
Answer:
see what you got to do is you have to find n
the mean age of 5 students whose ages are 8,x,13,12,and 10 is 10. calculate the value of x in years
Answers
Answer:
x = 7 years
Step-by-step explanation:
The mean (M) is defined as the average of the sum of all the data points in a set:
[tex]M=\frac{r_{1}...r_{n} }{n}[/tex]
Thus, since there are five data points and we're given the mean, we can use the following formula to find x:
[tex]M=10\\10=\frac{(8+x+13+12+10)}{5}\\ 50=43+x\\7=x[/tex]
how many ways are there to seat n couples around a circular table so that no couple sits together? (note: rotated seatings are considered to be the same, but reflected seatings are considered to be different.)
Answers
Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.
Let's consider the number of ways to seat n couples around a circular table without any restrictions first.
Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,
where we divide by 2n to account for rotations of the same seating arrangement.
Now, let's consider the restriction that no couple can sit together.
We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.
After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.
We can continue this process until all couples are seated.
Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:
[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]
We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.
Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.
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HELP PLS WILL GIVE BRAINLIST DUE TODAY AND SOON
Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| − 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answers
Answer:
A: description: graph of f(x) shifted left 3 units. Domain: (-∞, ∞); range: [0, ∞); vertex: (-3, 0).
B: description: graph of f(x) shifted down 2 units. Range: [-2, ∞); vertex: (0, -2).
Step-by-step explanation:
Given parent function f(x) = |x|, you want descriptions of g(x) = |x+3| and h(x) = |x| -2, including the vertex, domain, and range.
TransformationsThis question is concerned with translations of functions. The translations of interest are ...
f(x -h) — shifts the graph right h unitsf(x) +k — shifts the graph up k unitsAbsolute valueThe function f(x) = |x| is defined for all values of x. Its domain is all real numbers: (-∞, ∞). Shifting the function left or right does not affect the domain.
The vertex of the function is at (0, 0), and is a minimum. That means the range of the function is all non-negative numbers: [0, ∞). Shifting the function up or down affects the range by the same amount.
G(x)The function g(x) = |x+3| is equivalent to g(x) = f(x+3). Comparing to the transformations above, we see h = -3. So the graph of f(x) will be shifted left 3 units to make the graph of g(x).
vertex: (-3, 0)domain: (-∞, ∞)range: [0, ∞)H(x)The function h(x) = |x| -2 is equivalent to h(x) = f(x) -2. Comparing to the transformations above, we see k = -2. So the graph of f(x) wil be shifted down 2 units to make the graph of h(x).
vertex: (0, -2)range: [-2, ∞)The hour marks on a clock face are 30° apart. What is the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line?
Answers
So, the angle between the 4 o'clock and 12 o'clock marks is:
8 hours x 30 degrees/hour = 240 degrees
However, we need to find the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line. Since the clock face is circular, the line connecting the two marks is a chord of the circle. The angle between the chord and the horizontal line passing through the center of the circle is half the angle between the two marks.
Therefore, the angle we are looking for is:
240 degrees / 2 = 120 degrees
So, the line from the four o'clock mark to the twelve o'clock mark makes a 120-degree angle with a horizontal line.
Which function has real zeros at x = 3 and x = 7?f(x) = x2 4x – 21f(x) = x2 – 4x – 21f(x) = x2 – 10x 21f(x) = x2 – 10x – 21
Answers
Answer: The function that has real zeros at x = 3 and x = 7 is:
f(x) = (x - 3)(x - 7)
Expanding this function using FOIL (First, Outer, Inner, Last) method:
f(x) = x^2 - 10x + 21
Therefore, the answer is:
f(x) = x^2 - 10x + 21
Step-by-step explanation:
true or false the decimalformat class is part of the java api so it is automatically available to your programs.
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The statement is true. The DecimalFormat class is part of the Java API, specifically within java.text package, so it is automatically available to your programs. You can use it to format numbers in various ways, such as for displaying currency or percentages.
DecimalFormat is a concrete subclass of NumberFormat that formats decimal numbers. It has a variety of features designed to make it possible to parse and format numbers in any locale, including support for Western, Arabic, and Indic digits. It also supports different kinds of numbers, including integers (123), fixed-point numbers (123.4), scientific notation (1.23E4), percentages (12%), and currency amounts ($123). All of these can be localized.
To obtain a NumberFormat for a specific locale, including the default locale, call one of NumberFormat's factory methods, such as getInstance(). In general, do not call the DecimalFormat constructors directly, since the NumberFormat factory methods may return subclasses other than DecimalFormat. If you need to customize the format object, do something like this:
NumberFormat f = NumberFormat.getInstance(loc);
if (f instanceof DecimalFormat) {
((DecimalFormat) f).setDecimalSeparatorAlwaysShown(true);
}
A DecimalFormat comprises a pattern and a set of symbols. The pattern may be set directly using applyPattern(), or indirectly using the API methods. The symbols are stored in a DecimalFormatSymbols object. When using the NumberFormat factory methods, the pattern and symbols are read from localized ResourceBundles
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True. The Decimal Format class is a part of the Java API and is included in the java.text package.
It is automatically available to Java programs without the need for any additional installations or imports.
The Decimal Format class is part of the Java API, and it is automatically available to your programs.
The Java API is a collection of pre-written classes, methods, and interfaces that are part of the Java Development Kit (JDK).
These classes and methods provide a wide range of functionalities that can be utilized by Java developers to build robust applications.
The Decimal Format class, specifically, is a subclass of the Number Format class and is used to format decimal numbers according to a specific pattern.
The class provides methods to format and parse decimal numbers and can be used to specify the number of digits after the decimal point, the use of a thousand separator, and the currency symbol.
The Decimal Format class in your Java program, you simply need to import the class using the import statement, and then create an instance of the class.
For example:
import java. text. Decimal Format.
public class MyClass
{
public static void main (String [] args) {
Decimal Format df = new Decimal Format("#.00");
double num = 1234.5678
System.out.println(df.format(num));
}
}
The Decimal Format class using the import statement, and then create an instance of the class called df.
We then use the format method of the class to format the decimal number 1234.5678 with two decimal places.
The Decimal Format class is an essential part of the Java API and is automatically available to your programs.
Its inclusion in the Java API makes it easier for Java developers to format decimal numbers in their applications.
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Help asap I’m so lost
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The equation when solved for b gives ± 7√a/3. Option C
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.
They are also composed of arithmetic operations, such as;
AdditionBracketParenthesesSubtractionMultiplicationDivisionFrom the information given, we have;
9ab² = 49
To determine the value of b, take the following steps
Divide both sides by 9a
b² = 49/9a
Now, find the square root of both sides, we have;
b = [tex]\sqrt{\frac{49}{9a} }[/tex]
b = ± 7√a/3
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