First, we need to find the coordinates of each vertex of triangle ABC. Let's assume that A is located at (a,b), B is located at (c,d), and C is located at (e,f). Since we know the measures of the angles, we can also determine the slopes of the lines connecting the vertices:
The slope of line AB is (d-b)/(c-a), which is equal to tan(55°).
The slope of line BC is (f-d)/(e-c), which is equal to tan(80°).
The slope of line AC is (f-b)/(e-a), which is equal to tan(55°-45°) = tan(10°).
Using these slopes, we can find the equations of the three lines and solve for the coordinates of the vertices:
Line AB: y-b = tan(55°)(x-a)
Line BC: y-d = tan(80°)(x-c)
Line AC: y-b = tan(10°)(x-a)
Solving these equations simultaneously, we get:
A = (b + (c-a)tan(55°), b + (c-a)tan(55°-45°))
B = (c + (f-d)/tan(80°), d + (f-d))
C = (e + (b-f)/tan(10°), f + (e-a)tan(10°))
Next, we need to apply the rotation and reflection to these vertices to find the corresponding vertices of triangle XYZ. The rotation by 90° counterclockwise about the origin transforms a point (x,y) into (-y,x), while the reflection across the line y=x transforms a point (x,y) into (y,x). So:
Vertex A of ABC is mapped to vertex X of XYZ: (a,b) → (-b,a) → (a,-b)
Vertex B of ABC is mapped to vertex Y of XYZ: (c,d) → (-d,c) → (c,d)
Vertex C of ABC is mapped to vertex Z of XYZ: (e,f) → (-f,e) → (e,f)
Now we need to find the measure of angle Y. Since we don't know the exact coordinates of the vertices of XYZ, we'll use the fact that the rotation by 90° counterclockwise about the origin preserves angles and the reflection across the line y=x changes the orientation of angles but not their measure. Therefore:
m∠Y = m∠ZOX, where O is the origin
m∠ZOX = 90° - m∠XOZ
m∠XOZ = m∠COA = 55° + 45° = 100°
Therefore, m∠Y = 90° - 100° = -10°, but since angles can't have negative measures, we add 360° to get m∠Y = 350°.
So the measure of angle Y in triangle XYZ is 350°.
Question 1
1/1
Triangle ABC
maps to triangle XYZ
by a rotation of 90∘
counterclockwise about the origin followed by a reflection across the line y=x.
In triangle ABC,
m∠A=45∘,
m∠B=55∘,
and m∠C=80∘.
What is the measure of ∠Y?
Enter your answer as the correct value, like this: 42
55 is the answer I'm not joking try it lol
Drag each problem to show if the unknown quantity in the problem is a part, a whole, or a percent
Answer:
you didnt post a pic to show us the options
Step-by-step explanation:
didnt show the options so we cant help
Alex wants to fence in an area for a dog park. He has plotted three sides of the fenced area at the points E (1, 5), F (3, 5), and G (6, 1). He has 16 units of fencing. Where could Alex place point H so that he does not have to buy more fencing?
A. (0, 1)
B. (0, −2)
C. (1, 1)
D. (1, −2)
Answer:
C. (1, 1)
Step-by-step explanation:
first lets find how much fencing he has used between the three sides they gave us.
between E and F, there is 2 units.
between F and G, there is sqrt(3^2 + 4^2) = 5 units.
so, lets try option C.
between E and C, there is 4 units.
between C and C and G, there is 5 units.
2 + 5 + 4 + 5 = 16, which is how much fencing he has.
yes, it is C. (1, 1)
Which expression can be used to find the volume
of the rectangular prism in cubic centimeters?
Image shows a prism with a base area of 245 square cm and a height of 85 cm.
A.
85
+
245
B.
85
×
85
×
245
C.
85
+
(
85
×
245
)
D.
85
×
245
Answer: D. 85 ×245
is this help you give e hearts please
Answer:
D. 85 ×245
Question:
Which expression can be used to find the volume of the rectangular prism in cubic centimeters? The Image shows a prism with a base area of 245 square cm and a height of 85 cm.
The table shows values for functions f(x) and g(x) . x f(x) g(x) 1 14 14 3 −2 −4 5 5 −3 7 9 7 9 6 6 11 11 −3 What are the known solutions to f(x)=g(x) ? Select each correct answer. Responses 1 1 5 5 7 7 9 9 11 11
After observing the table of the given five functions, we know that the solution would be when f(x) = g(x) at x =1.
What are functions?A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The polynomial function of degree zero is a constant function.
Linear Function: The first-degree polynomial function.
Quadratic Function: The degree of two polynomial functions.
Cubic Function: The degree of three polynomial functions.
So, the table is shown:
x f(x) =4x+1 g(x) = 3ˣ⁺¹ ⁻ ⁴
-3 -11 -35/9
-2 -7 -11/3
-1 -3 -3
0 1 -1
1 5 5
2 9 23
3 13 77
We must resolve the equation f(x) = g. (x)
We must determine the value of x such that f(x) = g. (x).
You can see from the provided table that when x = 1
f(x) =5, g(x) = 5
Therefore, after observing the table of the given five functions, we know that the solution would be when f(x) = g(x) at x =1.
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Correct question:
The table shows values for functions f(x) and g(x)
x f(x)=4x+1 g(x)=3x+1−4
−3 −11 −359
−2 −7 −113
−1 −3 −3
0 1 −1
1 5 5
2 9 23
3 13 77
What is the solution to f(x)=g(x) ?
Select each correct answer.
−3
−2
−1
0
1
2
3
f(x)=3 squared root x + 11. Find the inverse of f(x)
Answer:
[tex] \frac{x {}^{2} }{9} - 11[/tex]
What are the measures of the missing angles? Please help
Answers:
s = 31
t = 62
u = 17
w = 31
================================================
Explanation:
Inscribed angles w and s subtend the same arc that the inscribed angle 31 degrees is doing. Therefore, angle w = angle s = 31 degrees.
Inscribed angles that subtend the same arc will be equal in measure.
Similarly, the 17 degree angle and angle u both subtend the same arc. This must mean angle u = 17 degrees.
------------
Use the inscribed angle theorem to determine the central angle t
angle t = 2*(inscribed angle w)
angle t = 2*(31)
angle t = 62 degrees
reggie is looking over his basketball statistics for the last 5 games , he scored the following number of points 12,15,18,20,5 .which of the following values calculated from his data set will not change if he scores 18 points in his next game ? A.the mean B.The medium C.the mode D.the range
In the mode values calculated from his data set will not change if he scores 18 points in his next game .
What in math is median?
When a data set's median value is used, 50% of the data points in the collection have values that are lower or equal to the median and 50% of them have values that are higher or equal to the median. When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.
12,15,18,20,5.
In ascending order = 5,12,15,18,20
A) Mean = 5 + 12 + 15 + 18 + 20/5
= 14
B) Median = 15
c) mode = no number is repeating
d) the range = 20 - 5 = 15
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Find the following. 2/5 of 240
Answer:
96
Step-by-step explanation:
2/5 of 240
2×240= 480
480÷5= 96
The triangles shown are congruent. Fill in the blank to complete the congruence statement for the triangles shown:
uze =
Answer:
uze=nkw
Step-by-step explanation:
U has no stroke which follows N
Z has a stroke which follows K
E has two strokes which follows W
Garnet has a container with cups of flour in it. She can make one dozen muffins with cups of flour. How many dozens of muffins can Garnet make with the flour she has?
Answer:
B is correct
Step-by-step explanation:
what is the formula for ASSUMED MEAN !!???
.
.
.
.
btw hello guyyzz !! < 3
please make me brainalist and keep smiling dude I hope you will be satisfied with my answer <3 :-)
Assumed Mean can be calculated using the formula a + (Σfidi /Σfi). Here, a denotes the assumed mean, fi is the frequency of the ith class, di is the deviation of the ith class, Σfi refers to the total number of observations and xi is the class mark.
The arithmetic mean of the grouped data is called the assumed mean
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 16 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the nearest tenth of a cubic foot?
This table shows the production possibility schedule for several toothpaste companies.
Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing small tubes of toothpaste.
From greatest comparative advantage to least comparative advantage the list of toothpaste is Mint, Fresh, Sparkling, Bright White
To determine the comparative advantage of toothpaste companies in producing small tubes of toothpaste, we need to look at the opportunity cost of producing small tubes of toothpaste in terms of the production of large tubes of toothpaste. The company with the lowest opportunity cost of producing small tubes of toothpaste (i.e., the company that gives up the least amount of large tubes of toothpaste to produce small tubes of toothpaste) has the greatest comparative advantage in producing small tubes of toothpaste. We can calculate the opportunity cost by looking at the difference in the number of large tubes of toothpaste that each company could produce if they chose to produce only large tubes versus the number of large tubes they could produce if they chose to produce some small tubes as well.
So, using the data provided in the table, we can calculate the opportunity cost for each company as follows:
Sparkling:
Opportunity cost of producing small tubes of toothpaste = (200 large tubes/hour - 100 large tubes/hour) / 200 small tubes/hour = 0.5 large tubes per small tube
Bright White:
Opportunity cost of producing small tubes of toothpaste = (250 large tubes/hour - 100 large tubes/hour) / 250 small tubes/hour = 0.6 large tubes per small tube
Fresh:
Opportunity cost of producing small tubes of toothpaste = (250 large tubes/hour - 200 large tubes/hour) / 250 small tubes/hour = 0.2 large tubes per small tube
Mint:
Opportunity cost of producing small tubes of toothpaste = (150 large tubes/hour - 150 large tubes/hour) / 150 small tubes/hour = 0 large tubes per small tube
Therefore, the order of the companies from greatest comparative advantage to least comparative advantage in producing small tubes of toothpaste is: Mint, Fresh, Sparkling, Bright White
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Complete question
Toothpaste company |Large tubes |Small tubes
Sparkling |100 per hour |200 per hour
Bright White |100 per hour | 250 per hour
Fresh |200 per hour |250 per hour
Mint |150 per hour |150 per hour
'This table shows the production possibility schedule for several toothpaste companies. Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing small tubes of toothpaste.
Which of the following pairs consists of equivalent fractions?
3/12 and 3/4
5/7 and 7/5
16/20 and 15/25
6/9 and 10/15
Answer:
16/20 and 15/25
Step-by-step explanation:
The solution is:
3/9 and 5/15 are the following pairs consists of equivalent fractions.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
12/20 and 20/25
1st fraction Divide by 4 , 2nd fraction Divide by 5
3/4 ≠ 4/5
5/6 and 6/5
5/6 ≠ 6/5
6/12 and 3/4
1st fraction Divide by 3
2/4 ≠ 3/4
3/9 and 5/15
1st fraction Divide by 3 , 2nd fraction Divide by 5
1/3 = 1/3
So, pair 3/9 and 5/15 is equivalent fractions
Hence, The solution is:
3/9 and 5/15 are the following pairs consists of equivalent fractions.
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complete question:
which of the following pairs consists of equivalent fractions. 12/20 snd 20/25, 5/6 and 6/5, 6/12 and 3/4, 3/9 and 5/15.
Work out the value of f in the following equation:
f sin 42° = 2.5
Give your answer to 2 d.p.
Answer:
f = 3.74
Step-by-step explanation:
f sin 42° = 2.5
f = 2.5 (sin 42° = 0.669)
sin 41°
= 3.736
= 3.74 (2.d.p.)
The value of f in the given equation is 3.74.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is,
f sin 42° = 2.5
Dividing both sides of the equation by sin 42°,
f = 2.5 / sin 42°
f = 3.74
Hence the value of f is 3.74.
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The circumference of a circle is 81.64 inches. What is the circle's radius? use 3.14 for pi
Answer:
13 cm
Step-by-step explanation:
c = Circumference=pid= 81.64 To find the radius of a circle you can just divide the diameter by 2.pi = 3.14d = diameter=c/3.14 Pi is always 3.14 or 22/7.d = 81.64/3.14d = 26r= radius= 26/2radius=13 cm
Answer: 13 inches
Step-by-step explanation:
You make $45.00 babysitting for eight hours. How much do you make per hour?
I make ------------- dollars per hour babysitting.
what is the rate of change between 75 and 125 miles driven
The rate of change between 75 and 125 miles is calculated by dividing the difference between the fuel cost at 125 and 75 miles by the distance traveled. The fuel cost at 75 miles is $3.85, while the fuel cost at 125 is $6.35. The rate of change is $0.05 per mile.
What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?To calculate the rate of change between 75 and 125 miles, subtract the fuel cost at 125 miles from the fuel cost at 75 miles and divide the difference by the distance travelled:
Rate of change = (fuel cost at 125 miles - fuel cost at 75 miles) / (125 - 75)
First, we need to find the fuel cost at 75 miles:
() = 0.1 + 0.05x
() = 0.1 + 0.05(75)
() = 3.85
The fuel cost at 75 miles is $3.85.
Next, we need to find the fuel cost at 125 miles:
() = 0.1 + 0.05x
() = 0.1 + 0.05(125)
() = 6.35
The fuel cost at 125 miles is $6.35.
Now we can substitute these values into the rate of change formula:
Rate of change = (6.35 - 3.85) / (125 - 75)
Rate of change = 2.5 / 50
Rate of change = 0.05
The rate of change of the cost of fuel when the car travels from 75 miles to 125 miles is $0.05 per mile.
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The complete question is: If a car travels x miles, the cost of fuel used is given by the function () = 0.1 + 0.05x dollars. What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
The statement which most closely summarizes the data is that about 80 necklaces have more than 28 beads. The solution has been obtained by using the standard deviation.
What is standard deviation?
The standard deviation measures how skewed the data are with respect to the mean. Data are said to be more densely grouped around the mean and more dispersed, respectively, when the standard deviation is low and large.
We are given that the mean for the normal distribution is 24 beads and the standard deviation is 4 beads.
Now,
⇒ P (X ≥ 28) = 1 - P (X < 28)
⇒ P (X ≥ 28) = 1 - P ([tex]\frac{X-24}{4}[/tex] < 1)
⇒ P (X ≥ 28) = 1 - P (Z < 1)
⇒ P (X ≥ 28) = 1 - 0.84
⇒ P (X ≥ 28) = 0.16
Now, since the total necklaces are 500, the necklaces which have more than 28 beads are as follows:
⇒ 500 * 0.16
⇒ 80 necklaces
Hence, the third option is the correct answer.
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Question: The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
A )About 24 necklaces have more than 28 beads.
B )About 48 necklaces have more than 28 beads.
C)About 80 necklaces have more than 28 beads.
D)About 96 necklaces have more than 28 beads.
2. For the table, identify the independent and dependent variables. Explain the relationship using words, and an equation (equation example: C = 2s + 20). Number of Snacks Purchased, "s" 1 2 3 Total Cost, $18 $21 $24 $27
The independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$". The relationship is linear, with $ = 3s + 15.
What is rate?A rate is a measure of the amount of change of one quantity with respect to another quantity, often expressed as a ratio or a fraction. It tells us how much one quantity changes per unit of time or per unit of another quantity. Examples of rates include speed, velocity, acceleration, interest rate, and growth rate
According to the given information:In the given table, the independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$".
The relationship between the number of snacks purchased and the total cost is a linear relationship, where the total cost increases by $3 for every additional snack purchased.
We can write the equation for the relationship between the two variables as:
$ = 3s + 15
Here, the constant term 15 represents the fixed cost or the cost of buying zero snacks. The coefficient 3 of the independent variable "s" represents the additional cost incurred for each additional snack purchased.
Therefore, The independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$". The relationship is linear, with $ = 3s + 15.
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A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 40 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 12 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 14 yards.
What is the area of the playground?
1,728 square yards
1,264 square yards
864 square yards
800 square yards
The area οf the playgrοund is 1264 square yards. Hence, οptiοn B is cοrrect.
What is the geοmetry?Geοmetry is a branch οf mathematics that deals with the study οf shapes, sizes, pοsitiοns, angles, and dimensiοns οf οbjects in space.
Tο find the area οf the playgrοund, we need tο divide it intο twο triangles and οne rectangle, and then find the area οf each and add them tοgether.
The rectangle has a length οf 12 yards and a width οf 20 yards, sο its area is:
40 x 20 = 800 square yards.
Area of Triangle 1 with base 40 yd and height 12 yd:
= 1/2 × 40 × 12
= 240 square yards.
Area of Triangle 2 with base (12 + 20) yd and height 14 yd:
= 1/2 × 32 × 14
= 224 square yards.
Adding all the areas:
= 800 + 240 + 224
= 1264 square yards.
Thus, the area of the playground is 1264 square yards. Hence, option B is correct.
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Complete question:
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
1,728 square yards
1,264 square yards
864 square yards
800 square yards
hi do you no what is 5364 rouded to the nearest thousand.
5,364 → 5,000
Therefore, 5,364 rounded to the nearest thousand is 5,000
Answer:
5000
Step-by-step explanation:
See, the thousands digit is not really in play, if the hundreds place is 5+, you raise the thousand up and if it's 4 or less, you round it down
Have you heard of 'five or more, raise the score, four or less, let it rest'
And for ex: 3678 rounded to the nearest thousand is 4000
The ratio of X to Y in a room is 6:5. If three boys leave the room, the ratio is 1:1. How many Y are in the room?
Answer:
15 Y (girls) in the room
Step-by-step explanation:
Given an initial ratio of boys : girls = 6 : 5 that becomes 1 : 1 when 3 boys leave the room, you want to know the number of girls in the room.
Ratio unitsThe initial difference in the number of ratio units is 6 -5 = 1. Removing 1 ratio unit from the "boys" side makes the ratio 5 : 5 = 1 : 1.
So, that 1 ratio unit corresponds to 3 boys. There are 5 ratio units of girls, so 3·5 = 15 girls.
There are 15 girls (Y) in the room.
__
Alternative solution
You could write an equation or two:
b/g = 6/5 . . . . . . initial ratio of boys/girls
(b-3)/g = 1/1 . . . . final ratio of boys/girls
Solving the first for b gives
b = 6/5g
Using that in the second gives ...
(6/5g -3) = g . . . . . . substitute for b, multiply by g
1/5g = 3 . . . . . . . . add 3-g
g = 15 . . . . . . . multiply by 5
Professor Melendez has 10 students in her college algebra class. Their ages are shown below.
When the outliers are removed, what is the mean age of the remaining students? 19.27 19.18.18.18.7.19.2018
The mean age of the students in the class is 22.3.
The median age of the students is 19.
What is the median age of the remaining students?
There are two ourers in the data from Professor
Melender's class: 27 and 47
The median age of the remaining students in Professor Melendez's college algebra class is 18.5.
To find the median age of the remaining students in Professor Melendez's college algebra class, we need to first remove the outliers, which are the ages of 27 and 47. After removing these outliers, we are left with 8 ages: 19, 18, 18, 18, 7, 19, 20, and 18. To find the median age, we need to arrange the ages in order from least to greatest. The ordered list of ages is: 7, 18, 18, 18, 19, 19, 20. Since there are an even number of ages, we need to find the average of the middle two ages, which are 18 and 19. Thus, the median age of the remaining students is (18 + 19) / 2 = 18.5.
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please help, I hate graph
The equation for the graph will be y = 10x.
How to solve for the linear equation provided in the excerpt?Let x be the number of T-shirts sold and y be the profit in dollars. Then, we can write the equation as:
y = (50/5)x
Simplifying the equation, we get:
y = 10x
To graph this linear equation, we can plot several points on the coordinate plane. For example, we need to plot points where x=0, y=0, x=1, y=10, x=2, y=20, and so on. We can then connect the points with a straight line to graph the equation. Check the attached document for clue.
The above answer is based on the question;
The profit for selling T-shirt at the school store is $50 for every 5 shirt. Write an equation and graph the relationship.
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a card is selected from a standard deck of cards. the probability the card is red or a king is (fraction).
The probability that a card drawn randomly from a standard deck of 52 cards is ed or a king = 7/13
We know that the formula for the probability of an event is given by,
P = number of favourable outcomes / total number of possible outcomes of an event
Let us assume that event A : drawing a red card
and event B: drawing a king card
Here, sample space is a standard deck of 52 cards.
So, n(S) = 52
We know that there are 26 red cards in a standard deck of cards.
So, n(A) = 26
And there are 4 kings
So, n(B) = 4
Since there are two cards of king are red and two are black.
The favorable number of cards = 26+2
=28
So, the required probability is:
P = 28/52
P = 7/13
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solve the system of inequalities for y+3x<5 and 1>2x-y ?
The shaded region is below both lines, and the boundary line y = 2x - 1 is dashed because the inequality is strict. The solution can be described as: y < 5 - 3x and y < 2x - 1.
What is inequality?Inequality is a mathematical statement that compares two values or expressions. It uses symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to indicate the relationship between the two expressions. Inequalities are used to represent a range of possible values, rather than just a single value as in an equation.
Here,
We have the system of inequalities:
y + 3x < 5
2x - y > 1
To solve this system, we can start by isolating y in each inequality:
y < 5 - 3x
y < 2x - 1
Now we can graph each inequality on the coordinate plane and shade the region that satisfies both inequalities.
For the first inequality y < 5 - 3x, we can start by graphing the line y = 5 - 3x. This line has a y-intercept of 5 and a slope of -3. Since the inequality is y < 5 - 3x, we need to shade the region below the line.
For the second inequality y < 2x - 1, we can start by graphing the line y = 2x - 1. This line has a y-intercept of -1 and a slope of 2. Since the inequality is 2x - y > 1, we need to shade the region below the line.
The solution to the system is the region that is shaded by both inequalities. Here is a graph of the solution:
| /
5 |- - - -/---- - - - - - - -
| / | /
| / | /
2 |- - - - -/------- - - - -
| / | /
|/ | /
-1 | - - - - - - - - - - - - -
0 1 2 3
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Carlos earns $50 000 each year as a shop clerk and an extra $1200 each year for gardening on the weekend
A, calculate his annual gross salary
B, use his gross salary to find his income tax
C, what is his annual income, after tax
D what is his fortnightly net income, to the nearest cent after tax?
Part A: annual gross salary = $51,200. Part B: income tax= $46,080
Part C: annual income, after tax reduction = $46,080.
Part D: fortnightly net income $126.24 per day.
Explain about the annual gross salary:Before taxes, benefits, and other wage garnishments are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account.
Given data:
Earning from shop clerk - $50,000 per year.
Earning from gardening - $1,200 per year.
Part A: annual gross salary.
annual gross salary = $50,000 + $1,200
annual gross salary = $51,200
Part B: income tax.
income tax = 10% of gross income
income tax = 0.10 * 51,200
income tax = $5,120
Part C: annual income, after tax reduction:
Net income = Gross income - tax
Net income = 51,200 - 5,120
Net income = $46,080
Part D: fortnightly net income:
fortnightly net income = Total net income / 365 days
fortnightly net income = $46,080 / 365
fortnightly net income = $126.24 per day.
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Complete question:
Carlos earns $50 000 each year as a shop clerk and an extra $1200 each year for gardening on the weekend. Tax applied is 10% on gross income.
A, calculate his annual gross salary
B, use his gross salary to find his income tax
C, what is his annual income, after tax
D what is his fortnightly net income, to the nearest cent after tax?
a bookstore took an inventory of the prices of its books and created a histogram to show the results. what shape does the distribution have?
The required shape of the attached histogram of the prices of the books is given as bell shaped.
General characteristics of histograms ,based on some general observations are,
If the histogram is roughly symmetric around its center, then the distribution is likely to be approximately normal (bell-shaped).
If the histogram has a peak on one side and a long tail on the other, then the distribution is likely to be skewed (either positively or negatively skewed).
If the histogram has multiple peaks or modes, then the distribution is likely to be multimodal.
Based on these observations,
The shape of the distribution in the bookstore's inventory is bell shaped.
As here in the attached histogram is symmetric around its center.
It is almost symmetric between 100 to 150 dollars.
Therefore, the shape of the distribution of the prices of books is bell shaped in the attached histogram.
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The above question is incomplete, the complete question is:
A bookstore took an inventory of the prices of its books and created a histogram to show the results. what shape does the distribution have?
Diagram is attached.
an elastic belt is placed around therein of a pulley of radius 5 cm one point of the belt is pulled directly away from the centre o of the pulley until its at p , 10 cm from o find the length of the best that is with the contact of rim of the pulley olso find the shaded region
The length of the best that is with the contact of rim of the pulley is (5/18)π cm.
The shaded region is 10√5 - (5/18)π cm.
How to calculate length of belt in a pulley?To find the length of the belt that is in contact with the rim of the pulley, we need to find the length of the arc of the circle with radius 5 cm that is between the points O and P.
The circumference of a circle with radius 5 cm is 2πr = 10π cm. So the fraction of the circle between O and P is 10/360 = 1/36 of the total circumference. Therefore, the length of the arc OP is (1/36) x 10π = (5/18)π cm.
To find the shaded region, we need to subtract the length of the belt in contact with the pulley from the length of the belt pulled to point P.
The belt pulled to point P is the hypotenuse of a right triangle with legs 5 cm (the radius of the pulley) and 10 cm (the distance from the center of the pulley to point P). Using the Pythagorean theorem, we can find the length of the belt pulled to point P:
h² = 5² + 10²
h² = 125
h = √125 = 5√5 cm
So the length of the belt pulled to point P is 2(5√5) = 10√5 cm.
Therefore, the length of the shaded region is 10√5 - (5/18)π cm. This is the length of the part of the belt that is not in contact with the pulley.
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